280 results
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2. Analysis of the Dynamical Properties of Discrete Predator-Prey Systems with Fear Effects and Refuges.
- Author
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Li, Wei, Zhang, Chunrui, and Wang, Mi
- Subjects
PREDATION ,DISCRETE systems ,BIFURCATION theory ,HOPF bifurcations ,LYAPUNOV exponents ,BIFURCATION diagrams ,COMPUTER simulation - Abstract
This paper examines the dynamic behavior of a particular category of discrete predator-prey system that feature both fear effect and refuge, using both analytical and numerical methods. The critical coefficients and properties of bifurcating periodic solutions for Flip and Hopf bifurcations are computed using the center manifold theorem and bifurcation theory. Additionally, numerical simulations are employed to illustrate the bifurcation phenomenon and chaos characteristics. The results demonstrate that period-doubling and Hopf bifurcations are two typical routes to generate chaos, as evidenced by the calculation of the maximum Lyapunov exponents near the critical bifurcation points. Finally, a feedback control method is suggested, utilizing feedback of system states and perturbation of feedback parameters, to efficiently manage the bifurcations and chaotic attractors of the discrete predator-prey model. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
3. Dynamics Analysis of a Delayed Crimean-Congo Hemorrhagic Fever Virus Model in Humans.
- Author
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Al-Jubouri, Karrar Qahtan and Naji, Raid Kamel
- Subjects
HEMORRHAGIC fever ,BASIC reproduction number ,HOPF bifurcations ,INFECTIOUS disease transmission ,DISEASE vectors ,VIRUS diseases - Abstract
Given that the Crimean and Congo hemorrhagic fever is one of the deadly viral diseases that occur seasonally due to the activity of the carrier "tick," studying and developing a mathematical model simulating this illness are crucial. Due to the delay in the disease's incubation time in the sick individual, the paper involved the development of a mathematical model modeling the transmission of the disease from the carrier to humans and its spread among them. The major objective is to comprehend the dynamics of illness transmission so that it may be controlled, as well as how time delay affects this. The discussion of every one of the solution's qualitative attributes is included. According to the established basic reproduction number, the stability analysis of the endemic equilibrium point and the disease-free equilibrium point is examined for the presence or absence of delay. Hopf bifurcation's triggering circumstance is identified. Using the center manifold theorem and the normal form, the direction and stability of the bifurcating Hopf bifurcation are explored. The next step is sensitivity analysis, which explains the set of control settings that have an impact on how the system behaves. Finally, to further comprehend the model's dynamical behavior and validate the discovered analytical conclusions, numerical simulation has been used. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
4. A Malware Propagation Model with Dual Delay in the Industrial Control Network.
- Author
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Yang, Wei, Fu, Qiang, and Yao, Yu
- Subjects
HOPF bifurcations ,MALWARE ,DYNAMICAL systems ,INDUSTRIAL security - Abstract
The malware attacks targeting the industrial control network are gradually increasing, and the nonlinear phenomenon makes it difficult to predict the propagation behavior of malware. Once the dynamic system becomes unstable, the propagation of malware will be out of control, which will seriously threaten the security of the industrial control network. So, it is necessary to model and study the propagation of malware in the industrial control network. In this paper, a SIDQR model with dual delay is proposed by fully considering the characteristics of the industrial control network. By analyzing the nonlinear dynamics of the model, the Hopf bifurcation is discussed in detail when the value of dual delay is greater than zero, and the expression for the threshold is also provided. The results of the experiments indicate that the system may have multiple bifurcation points. By comparing different immune and quarantine rates, it is found that the immune rate can be appropriately increased and the isolation rate can be appropriately reduced in the industrial control network, which can suppress the spread of malware without interrupting the industrial production. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
5. Stability and Hopf Bifurcation Analysis of an Oncolytic Virus Infection Model with Two Time Delays and Saturation Incidence.
- Author
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Liu, Xia and Hu, Zhixing
- Subjects
HOPF bifurcations ,ONCOGENIC viruses ,VIRUS diseases ,SYSTEM dynamics ,TREATMENT effectiveness - Abstract
In this paper, we study a model of oncolytic virus infection with two time delays, one of which is the time from the entry of viruses into tumor cells to start gene replication, and the other is the time from the entry of viruses into tumor cells to release new virus particles by infected tumor cells. In previous studies on oncolytic virus infection models, the infection rate was linear. Combined with the virus infection models, the saturated infection rate, β T V / 1 + q V is further considered to describe the dynamic evolution between viruses and tumor cells more objectively so as to further study the therapeutic effect of oncolytic viruses. This paper discusses the dynamics of the system under three conditions: (1) τ 1 = τ 2 = 0 , (2) τ 1 = 0 and τ 2 > 0 , and (3) τ 1 > 0 and τ 2 > 0 , and proves the global stability and local stability of the virusfree equilibrium, the stability of the infection equilibrium, and the existence of Hopf bifurcation. Finally, the conclusions of the paper are verified by MATLAB numerical simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
6. The Dynamics of a Delayed Ecoepidemiological Model with Nonlinear Incidence Rate.
- Author
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Hussien, Reem Mudar and Naji, Raid Kamel
- Subjects
HOPF bifurcations ,INFECTIOUS disease transmission ,COMPUTER simulation - Abstract
In this paper, the general framework for calculating the stability of equilibria, Hopf bifurcation of a delayed prey-predator system with an SI type of disease in the prey population, is investigated. The impact of the incubation period delay on disease transmission utilizing a nonlinear incidence rate was taken into account. For the purpose of explaining the predation process, a modified Holling type II functional response was used. First, the existence, uniform boundedness, and positivity of the solutions of the considered model system, along with the behavior of equilibria and the existence of Hopf bifurcation, are studied. The critical values of the delay parameter for which stability switches and the nature of the Hopf bifurcation by using normal form theory and center manifold theorem are identified. Additionally, using numerical simulations and a hypothetical dataset, various dynamic characteristics are discovered, including stability switches, chaos, and Hopf bifurcation scenarios. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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7. Control Scheme for a Fractional-Order Chaotic Genesio-Tesi Model.
- Author
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Xu, Changjin, Li, Peiluan, Liao, Maoxin, Liu, Zixin, Xiao, Qimei, and Yuan, Shuai
- Subjects
TIME delay systems ,HOPF bifurcations ,IMAGE encryption ,FRACTIONAL programming ,STABILITY criterion ,COMPUTER simulation - Abstract
In this paper, based on the earlier research, a new fractional-order chaotic Genesio-Tesi model is established. The chaotic phenomenon of the fractional-order chaotic Genesio-Tesi model is controlled by designing two suitable time-delayed feedback controllers. With the aid of Laplace transform, we obtain the characteristic equation of the controlled chaotic Genesio-Tesi model. Then by regarding the time delay as the bifurcation parameter and analyzing the characteristic equation, some new sufficient criteria to guarantee the stability and the existence of Hopf bifurcation for the controlled fractional-order chaotic Genesio-Tesi model are derived. The research shows that when time delay remains in some interval, the equilibrium point of the controlled chaotic Genesio-Tesi model is stable and a Hopf bifurcation will happen when the time delay crosses a critical value. The effect of the time delay on the stability and the existence of Hopf bifurcation for the controlled fractional-order chaotic Genesio-Tesi model is shown. At last, computer simulations check the rationalization of the obtained theoretical prediction. The derived key results in this paper play an important role in controlling the chaotic behavior of many other differential chaotic systems. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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8. Spatiotemporal Patterns Induced by Hopf Bifurcations in a Homogeneous Diffusive Predator-Prey System.
- Author
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Lin, Meng, Chai, Yanyou, Yang, Xuguang, and Wang, Yufeng
- Subjects
PREDATION ,NEUMANN boundary conditions ,BIFURCATION theory ,HOPF bifurcations ,DYNAMICAL systems ,SQUARE root - Abstract
In this paper, we consider a diffusive predator-prey system where the prey exhibits the herd behavior in terms of the square root of the prey population. The model is supposed to impose on homogeneous Neumann boundary conditions in the bounded spatial domain. By using the abstract Hopf bifurcation theory in infinite dimensional dynamical system, we are capable of proving the existence of both spatial homogeneous and nonhomogeneous periodic solutions driven by Hopf bifurcations bifurcating from the positive constant steady state solutions. Our results allow for the clearer understanding of the mechanism of the spatiotemporal pattern formations of the predator-prey interactions in ecology. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
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9. Modeling and Analysis of Predator-Prey Model with Fear Effect in Prey and Hunting Cooperation among Predators and Harvesting.
- Author
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Belew, Basaznew and Melese, Dawit
- Subjects
HARVESTING ,PREDATION ,PREDATORY animals ,HOPF bifurcations ,HUNTING - Abstract
In this paper, we present and analyze predator-prey system where prey population is linearly harvested and affected by fear and the prey population has grown logistically in the absence of predators. The predator population follows hunting cooperation, and it predates the prey population in the Holling type II functional responses. Based on those assumptions, a two-dimensional mathematical model is derived. The positivity, boundedness, and extinction of both prey and predator populations of the solution of the system are discussed. The existence, stability (local and global), and the Hopf bifurcation analysis of the biologically feasible equilibrium points are investigated. The aim of this research is to explore the effect of fear on the prey population and hunting cooperation on the predator population, and both prey and predator populations are harvested linearly and taken as control parameters of the model. If the values of c 1 > 1 , then both prey and predator populations are extinct and also fear parameter has a stabilizing effect on system 4. From the numerical simulation, it was found that the fear effect, hunting cooperation, prey harvesting, and predator harvesting change the dynamics of system 4. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
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10. Bifurcations of a Fractional-Order Four-Neuron Recurrent Neural Network with Multiple Delays.
- Author
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Fei, Yu, Li, Rongli, Meng, Xiaofang, and Li, Zhouhong
- Subjects
RECURRENT neural networks ,HOPF bifurcations ,NEURAL circuitry - Abstract
This paper investigates the bifurcation issue of fractional-order four-neuron recurrent neural network with multiple delays. First, the stability and Hopf bifurcation of the system are studied by analyzing the associated characteristic equations. It is shown that the dynamics of delayed fractional-order neural networks not only depend heavily on the communication delay but also significantly affects the applications with different delays. Second, we numerically demonstrate the effect of the order on the Hopf bifurcation. Two numerical examples illustrate the validity of the theoretical results at the end. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
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11. A Fractional-Order Discrete Lorenz Map.
- Author
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Xie, Yanyun
- Subjects
HOPF bifurcations ,CHAOS synchronization ,COMPUTER simulation - Abstract
In this paper, a discrete Lorenz map with the fractional difference is analyzed. Bifurcations of the map in commensurate-order and incommensurate-order cases are studied when an order and a parameter are varied. Hopf bifurcation and periodic-doubling cascade are found by the numerical simulations. The parameter values of Hopf bifurcation points are determined when the order is taken as a different value. It can be concluded that the parameter decreases as the order increases. Chaos control and synchronization for the fractional-order discrete Lorenz map are studied through designing the suitable controllers. The effectiveness of the controllers is illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
12. Stability and Bifurcation for a Single-Species Model with Delay Weak Kernel and Constant Rate Harvesting.
- Author
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Li, Xiangrui and Huang, Shuibo
- Subjects
HOPF bifurcations ,COMPUTER simulation ,RATES - Abstract
In this paper, we consider the effect of constant rate harvesting on the dynamics of a single-species model with a delay weak kernel. By a simple transformation, the single-species model is transformed into a two-dimensional system. The existence and the stability of possible equilibria under different conditions are carried out by analysing the two-dimensional system. We show that there exists a critical harvesting value such that the population goes extinct in finite time if the constant rate harvesting u is greater than the critical value, and there exists a degenerate critical point or a saddle-node bifurcation when the constant rate harvesting u equals the critical value. When the constant rate harvesting u is less than the critical value, sufficient conditions about the existence of the Hopf bifurcation are derived by topological normal form for the Hopf bifurcation and calculating the first Lyapunov coefficient. The key results obtained in the present paper are illustrated using numerical simulations. These results indicate that it is important to select the appropriate constant rate harvesting u. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
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13. Bifurcation Analysis of a 5D Nutrient, Plankton, Limnothrissa miodon Model with Hydrocynus vittatus Predation.
- Author
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Mutasa, Farikayi K., Jones, Brian, Tendaupenyu, Itai H., Nhiwatiwa, Tamuka, and Ndebele-Murisa, Mzime R.
- Subjects
HOPF bifurcations ,PREDATION ,PLANKTON ,MATHEMATICAL models ,ZOOPLANKTON - Abstract
In this paper, we construct and analyze a theoretical, deterministic 5 D mathematical model of Limnothrissa miodon with nutrients, phytoplankton, zooplankton, and Hydrocynus vittatus predation. Local stability analysis results agree with the numerical simulations in that the coexistence equilibrium is locally stable provided that certain conditions are satisfied. The coexistence equilibrium is globally stable if certain conditions are met. Existence, stability, and direction of Hopf bifurcations are derived for some parameters. Bifurcation analysis shows that the model undergoes Hopf bifurcation at the coexistence point for the zooplankton growth rate with periodic doubling leading to chaos. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
14. Bifurcation of a Fractional-Order Delayed Malware Propagation Model in Social Networks.
- Author
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Xu, Changjin, Liao, Maoxin, and Li, Peiluan
- Subjects
INTERNET of things ,COMPUTER network security ,MALWARE ,HOPF bifurcations ,COMPUTER simulation - Abstract
In recent years, with the rapid development of the Internet and the Internet of Things, network security is urgently needed. Malware becomes a major threat to network security. Thus, the study on malware propagation model plays an important role in network security. In the past few decades, numerous researchers put up various kinds of malware propagation models to analyze the dynamic interaction. However, many works are only concerned with the integer-order malware propagation models, while the investigation on fractional-order ones is very few. In this paper, based on the earlier works, we will put up a new fractional-order delayed malware propagation model. Letting the delay be bifurcation parameter and analyzing the corresponding characteristic equations of considered system, we will establish a set of new sufficient conditions to guarantee the stability and the existence of Hopf bifurcation of fractional-order delayed malware propagation model. The study shows that the delay and the fractional order have important effect on the stability and Hopf bifurcation of considered system. To check the correctness of theoretical analyses, we carry out some computer simulations. At last, a simple conclusion is drawn. The derived results of this paper are completely innovative and play an important guiding role in network security. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
15. Modeling and Mathematical Analysis of Labor Force Evolution.
- Author
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ElFadily, Sanaa and Kaddar, Abdelilah
- Subjects
LABOR supply ,HOPF bifurcations ,BIFURCATION theory ,COMPUTER simulation ,MATHEMATICAL analysis - Abstract
In this paper, we propose a delayed differential system to model labor force (occupied labor force and unemployed) evolution. The mathematical analysis of our model focuses on the local behavior of the labor force around a positive equilibrium position; the existence of a branch of periodic solutions bifurcated from the positive equilibrium is then analyzed according to the Hopf bifurcation theorem. Finally, we performed numerical simulations to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
16. Stability and Hopf Bifurcation of a Delayed Epidemic Model of Computer Virus with Impact of Antivirus Software.
- Author
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Zhang, Zizhen, Upadhyay, Ranjit Kumar, Bi, Dianjie, and Wei, Ruibin
- Subjects
HOPF bifurcations ,ANTIVIRUS software ,COMPUTER simulation ,INTERNET ,LYAPUNOV functions - Abstract
In this paper, we investigate an SLBRS computer virus model with time delay and impact of antivirus software. The proposed model considers the entering rates of all computers since every computer can enter or leave the Internet easily. It has been observed that there is a stability switch and the system becomes unstable due to the effect of the time delay. Conditions under which the system remains locally stable and Hopf bifurcation occurs are found. Sufficient conditions for global stability of endemic equilibrium are derived by constructing a Lyapunov function. Formulae for the direction, stability, and period of the bifurcating periodic solutions are conducted with the aid of the normal form theory and center manifold theorem. Numerical simulations are carried out to analyze the effect of some of the parameters in the system on the dynamic behavior of the system. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
17. Analysis of a Tuberculosis Infection Model considering the Influence of Saturated Recovery (Treatment).
- Author
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Sulayman, Fatima and Abdullah, Farah Aini
- Subjects
TUBERCULOSIS ,MYCOBACTERIUM tuberculosis ,HOPF bifurcations ,INFECTION ,LYAPUNOV functions - Abstract
Tuberculosis (TB) is a serious global health threat that is caused by the bacterium Mycobacterium tuberculosis, is extremely infectious, and has a high mortality rate. In this paper, we developed a model of TB infection to predict the impact of saturated recovery. The existence of equilibrium and its stability has been investigated based on the effective reproduction number R C . The model displays interesting dynamics, including backward bifurcation and Hopf bifurcation, which further results in the stable disease-free and stable endemic equilibria to be coexisting. Bifurcation analysis demonstrates that the saturation parameter is accountable for the phenomenon of backward bifurcation. We derive a condition that guarantees that the model is globally asymptotically stable using the Lyapunov function approach to global stability. The numerical simulation also reveals that the extent of saturation of TB infection is the mechanism that is fuelling TB disease in the population. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
18. Study on a Class of Piecewise Nonlinear Systems with Fractional Delay.
- Author
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Wang, Meiqi, Ma, Wenli, Chen, Enli, and Chang, Yujian
- Subjects
- *
NONLINEAR systems , *TIME delay systems , *HOPF bifurcations , *BIFURCATION theory , *DYNAMIC models - Abstract
In this paper, a dynamic model of piecewise nonlinear system with fractional-order time delay is simplified. The amplitude frequency response equation of the dynamic model of piecewise nonlinear system with fractional-order time delay under periodic excitation is obtained by using the average method. It is found that the amplitude of the system changes when the external excitation frequency changes. At the same time, the amplitude frequency response characteristics of the system under different time delay parameters, different fractional-order parameters, and coefficient are studied. By analyzing the amplitude frequency response characteristics, the influence of time delay and fractional-order parameters on the stability of the system is analyzed in this paper, and the bifurcation equations of the system are studied by using the theory of continuity. The transition sets under different piecewise states and the constrained bifurcation behaviors under the corresponding unfolding parameters are obtained. The variation of the bifurcation topology of the system with the change of system parameters is given. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
19. Bifurcation Analysis of a Two-Dimensional Neuron Model under Electrical Stimulation.
- Author
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Yuan, Chunhua and Li, Xiangyu
- Subjects
TWO-dimensional models ,NEURON analysis ,HOPF bifurcations ,ACTION potentials ,BEHAVIORAL research - Abstract
The two-dimensional neuron model can not only reproduce abundant firing patterns, but also satisfy the research of dynamical behavior because of its nonlinear characteristics. It is the most simplified model that includes the fast and slow variables required for neuron firing. In this paper, the dynamic characteristics of two-dimensional neuron model are described by both analytical and numerical methods, and the influence of model parameters and external stimuli on dynamic characteristics is described. The firing characteristics of the Prescott model under external electrical stimulation are studied, and the influence of electrophysiological parameters on the firing characteristics is analyzed. The saddle-node bifurcation and Hopf bifurcation characteristics are studied through the distribution of equilibrium points. It is found that there are critical saddle-node bifurcation and critical Hopf bifurcation in the Prescott model. And the value range of the key parameters that cause the critical bifurcation of the model is obtained by analytical methods. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
20. Hopf Bifurcation of a Delayed Ecoepidemic Model with Ratio-Dependent Transmission Rate.
- Author
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Xia, Wanjun, Kundu, Soumen, and Maitra, Sarit
- Subjects
HOPF bifurcations ,TIME delay systems ,EXISTENCE theorems ,PARAMETERS (Statistics) ,COMPUTER simulation - Abstract
A delayed ecoepidemic model with ratio-dependent transmission rate has been proposed in this paper. Effects of the time delay due to the gestation of the predator are the main focus of our work. Sufficient conditions for local stability and existence of a Hopf bifurcation of the model are derived by regarding the time delay as the bifurcation parameter. Furthermore, properties of the Hopf bifurcation are investigated by using the normal form theory and the center manifold theorem. Finally, numerical simulations are carried out in order to validate our obtained theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
21. Delay Feedback Control of the Lorenz-Like System.
- Author
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Chen, Qin and Gao, Jianguo
- Subjects
FEEDBACK control systems ,HOPF bifurcations ,FUNCTIONAL differential equations ,CENTER manifolds (Mathematics) ,COMPUTER simulation - Abstract
We choose the delay as a variable parameter and investigate the Lorentz-like system with delayed feedback by using Hopf bifurcation theory and functional differential equations. The local stability of the positive equilibrium and the existence of Hopf bifurcations are obtained. After that the direction of Hopf bifurcation and stability of periodic solutions bifurcating from equilibrium is determined by using the normal form theory and center manifold theorem. In the end, some numerical simulations are employed to validate the theoretical analysis. The results show that the purpose of controlling chaos can be achieved by adjusting appropriate feedback effect strength and delay parameters. The applied delay feedback control method in this paper is general and can be applied to other nonlinear chaotic systems. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
22. Control of Hopf Bifurcation Type of a Neuron Model Using Washout Filter.
- Author
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Yuan, Chunhua and Li, Xiangyu
- Subjects
HOPF bifurcations ,NEURONS ,ELECTRIC stimulation ,TWO-dimensional models ,MATHEMATICAL models ,INFANT formulas - Abstract
A quantitative mathematical model of neurons should not only include enough details to consider the dynamics of single neurons but also minimize the complexity of the model so that the model calculation is convenient. The two-dimensional Prescott model provides a good compromise between the authenticity and computational efficiency of a neuron. The dynamic characteristics of the Prescott model under external electrical stimulation are studied by combining analytical and numerical methods in this paper. Through the analysis of the equilibrium point distribution, the influence of model parameters and external stimulus on the dynamic characteristics is described. The occurrence conditions and the type of Hopf bifurcation in the Prescott model are analyzed, and the analytical determination formula of the Hopf bifurcation type in the neuron model is obtained. Washout filter control is used to change the Hopf bifurcation type, so that the subcritical Hopf bifurcation transforms to supercritical Hopf bifurcation, so as to realize the change of the dynamic characteristics of the model. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
23. Complexity Analysis of a Modified Predator-Prey System with Beddington–DeAngelis Functional Response and Allee-Like Effect on Predator.
- Author
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Wang, Shuangte and Yu, Hengguo
- Subjects
PREDATION ,HOPF bifurcations ,NUMERICAL analysis ,PREDATORY animals ,COMPUTER simulation - Abstract
In this paper, complex dynamical behaviors of a predator-prey system with the Beddington–DeAngelis functional response and the Allee-like effect on predator were studied by qualitative analysis and numerical simulations. Theoretical derivations have given some sufficient and threshold conditions to guarantee the occurrence of transcritical, saddle-node, pitchfork, and nondegenerate Hopf bifurcations. Computer simulations have verified the feasibility and effectiveness of the theoretical results. In short, we hope that these works could provide a theoretical basis for future research of complexity in more predator-prey ecosystems. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
24. Emergence of Beta Oscillations of a Resonance Model for Parkinson's Disease.
- Author
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Chen, Yaqian, Wang, Junsong, Kang, Yanmei, and Ghori, Muhammad Bilal
- Subjects
RESONANT vibration ,PARKINSON'S disease ,HOPF bifurcations ,NEURAL transmission ,OSCILLATIONS - Abstract
In Parkinson's disease, the excess of beta oscillations in cortical-basal ganglia (BG) circuits has been correlated with normal movement suppression. In this paper, a physiologically based resonance model, generalizing an earlier model of the STN-GPe circuit, is employed to analyze critical dynamics of the occurrence of beta oscillations, which correspond to Hopf bifurcation. With the experimentally measured parameters, conditions for the occurrence of Hopf bifurcation with time delay are deduced by means of linear stability analysis, center manifold theorem, and normal form analysis. It is found that beta oscillations can be induced by increasing synaptic transmission delay. Furthermore, it is revealed that the oscillations originate from interaction among different synaptic connections. Our analytical results are consistent with the previous experimental and simulating findings, thus may provide a more systematic insight into the mechanisms underlying the transient beta bursts. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
25. Dynamics Analysis of a Mathematical Model for New Product Innovation Diffusion.
- Author
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Li, Chunru and Ma, Zujun
- Subjects
CONTINUOUS time models ,MATHEMATICAL analysis ,MATHEMATICAL models ,NEW product development ,HOPF bifurcations ,DIFFUSION of innovations - Abstract
In this paper, a mathematical model with time-delay-related parameters and media coverage to describe the diffusion process of new products is proposed, in which the time-delay-related parameters denote the stage in which potential customers decide whether to adopt a new product. Then, the stability and the Hopf bifurcation of the proposed model are analyzed in detail. The center manifold theorem and the normal form theory are used to investigate the stability of the bifurcating periodic solution. Moreover, a numerical simulation is conducted to investigate the difference between the model with delay-dependent parameters and that with delay-independent parameters. The results show that there is significant difference between the two models. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
26. Qualitative Analysis of the Effect of Weeds Removal in Paddy Ecosystems in Fallow Season.
- Author
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Zhou, Leru, Liu, Zhigang, and Zhou, Tiejun
- Subjects
WEEDS ,PADDY fields ,HOPF bifurcations ,DIFFERENTIAL equations ,ECOSYSTEMS - Abstract
In the paper, we introduce a differential equations model of paddy ecosystems in the fallow season to study the effect of weeds removal from the paddy fields. We found that there is an unstable equilibrium of the extinction of weeds and herbivores in the system. When the intensity of weeds removal meets certain conditions and the intrinsic growth rate of herbivores is higher than their excretion rate, there is a coexistence equilibrium state in the system. By linearizing the system and using the Routh–Hurwitz criterion, we obtained the local asymptotically stable conditions of the coexistence equilibrium state. The critical value formula of the Hopf bifurcation is presented too. The model demonstrates that weeds removal from paddy fields could largely reduce the weeds biomass in the equilibrium state, but it also decreases the herbivore biomass, which probably reduces the content of inorganic fertilizer in the soil. We found a particular intensity of weeds removal that could result in the minimum content of inorganic fertilizer, suggesting weeds removal should be kept away from this intensity. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
27. Nonlinear Dynamics in a Chemical Reaction under an Amplitude-Modulated Excitation: Hysteresis, Vibrational Resonance, Multistability, and Chaos.
- Author
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Monwanou, A. V., Koukpémèdji, A. A., Ainamon, C., Nwagoum Tuwa, P. R., Miwadinou, C. H., and Chabi Orou, J. B.
- Subjects
CHEMICAL reactions ,HYSTERESIS ,RESONANCE ,LYAPUNOV exponents ,HOPF bifurcations - Abstract
This paper deals with the effects of an amplitude-modulated (AM) excitation on the nonlinear dynamics of reactions between four molecules. The computation of the fixed points of the autonomous nonlinear chemical system has been made in detail using the Cardan's method. Hopf bifurcation has been also successfully checked. Routes to chaos have been investigated through bifurcations structures, Lyapunov exponent, phase portraits, and Poincaré section. The effects of the control force on chaotic motions have been strongly analyzed, and the control efficiency is found in the cases g = 0 (unmodulated case) and g ≠ 0 with Ω = ω and Ω / w ≠ p / q ; p and q are simple positive integers. Vibrational resonance (VR), hysteresis, and coexistence of several attractors have been studied in detail based on the relationship between the frequencies of the AM force. Results of analytical investigations are validated and complemented by numerical simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
28. Complexity Induced by External Stimulations in a Neural Network System with Time Delay.
- Author
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Zhen, Bin, Zhang, Dingyi, and Song, Zigen
- Subjects
TIME delay systems ,HOPF bifurcations ,NUMERICAL analysis ,SYSTEM dynamics - Abstract
Complexity and dynamical analysis in neural systems play an important role in the application of optimization problem and associative memory. In this paper, we establish a delayed neural system with external stimulations. The complex dynamical behaviors induced by external simulations are investigated employing theoretical analysis and numerical simulation. Firstly, we illustrate number of equilibria by the saddle-node bifurcation of nontrivial equilibria. It implies that the neural system has one/three equilibria for the external stimulation. Then, analyzing characteristic equation to find Hopf bifurcation, we obtain the equilibrium's stability and illustrate periodic activity induced by the external stimulations and time delay. The neural system exhibits a periodic activity with the increased delay. Further, the external stimulations can induce and suppress the periodic activity. The system dynamics can be transformed from quiescent state (i.e., the stable equilibrium) to periodic activity and then quiescent state with stimulation increasing. Finally, inspired by ubiquitous rhythm in living organisms, we introduce periodic stimulations with low frequency as rhythm activity from sensory organs and other regions. The neural system subjected by the periodic stimulations exhibits some interesting activities, such as periodic spiking, subthreshold oscillation, and bursting-like activity. Moreover, the subthreshold oscillation can switch its position with delay increasing. The neural system may employ time delay to realize Winner-Take-All functionality. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
29. Hopf Bifurcation on a Cancer Therapy Model by Oncolytic Virus Involving the Malignancy Effect and Therapeutic Efficacy.
- Author
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Adi-Kusumo, F., Aryati, L., Risdayati, S., and Norhidayah, S.
- Subjects
TREATMENT effectiveness ,HOPF bifurcations ,CANCER treatment ,CELL populations ,CANCER ,LOTKA-Volterra equations - Abstract
We introduce a mathematical model that shows the interaction dynamics between the uninfected and the infected cancer cell populations with oncolytic viruses for the benign and the malignant cancer cases. There are two important parameters in our model that represent the malignancy level of the cancer cells and the efficacy of the therapy. The parameters play an important role to determine the possibility to have successful therapy for cancer. Our model is based on the predator-prey model with logistic growth, functional response, and the saturation effect that show the possibility for the virus to be deactivated and blocked by the human immune system after they reach a certain value. In this paper, we consider the appearance of the Hopf bifurcation on the system to characterize the treatment response based on the malignancy effect of the disease. We employ numerical bifurcation analysis when the value of the malignancy parameter is varied to understand the dynamics of the system. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
30. Complex Behavior Analysis of a Fractional-Order Land Dynamical Model with Holling-II Type Land Reclamation Rate on Time Delay.
- Author
-
Wu, Li, Li, Zhouhong, Zhang, Yuan, and Xie, Binggeng
- Subjects
BEHAVIORAL assessment ,HOPF bifurcations ,RECLAMATION of land ,MATHEMATICAL complex analysis ,STABILITY criterion ,REHABILITATION technology - Abstract
In this paper, a fractional-order land model with Holling-II type transformation rate and time delay is investigated. First of all, the variable-order fractional derivative is defined in the Caputo type. Second, by applying time delay as the bifurcation parameter, some criteria to determine the stability and Hopf bifurcation of the model are presented. It turns out that the time delay can drive the model to be oscillatory, even when its steady state is stable. Finally, one numerical example is proposed to justify the validity of theoretical analysis. These results may provide insights to the development of a reasonable strategy to control land-use change. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
31. A Torus-Chaotic System and Its Pseudorandom Properties.
- Author
-
Liu, Jizhao, Zhang, Xiangzi, Zhao, Qingchun, Lian, Jing, Huang, Fangjun, and Ma, Yide
- Subjects
LYAPUNOV exponents ,RANDOM number generators ,ALGORITHMS ,INTERNET security ,SECURITY systems ,HOPF bifurcations - Abstract
Exploring and investigating new chaotic systems is a popular topic in nonlinear science. Although numerous chaotic systems have been introduced in the literature, few of them focus on torus-chaotic system. The aim of our short work is to widen the current knowledge of torus chaos. In this paper, a new torus-chaotic system is proposed, which has one positive Lyapunov exponent, two zero Lyapunov exponents, and two negative Lyapunov exponents. The dynamic behavior is investigated by Lyapunov exponents, bifurcations, and stability. The analysis shows that this system has an interesting route leading to chaos. Furthermore, the pseudorandom properties of output sequence are well studied and a random number generator algorithm is proposed, which has the potential of being used in several cyber security systems such as the verification code, secure QR code, and some secure communication protocols. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
32. Bifurcation Control of a Delayed Fractional Mosaic Disease Model for Jatropha curcas with Farming Awareness.
- Author
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Liu, Shouzong, Huang, Mingzhan, and Wang, Juan
- Subjects
MOSAIC diseases ,JATROPHA ,MEDICAL model ,HOPF bifurcations ,MOSAIC viruses ,VIRUS diseases ,PSYCHOLOGICAL feedback ,BASIC reproduction number - Abstract
In this paper, the bifurcation control of a fractional-order mosaic virus infection model for Jatropha curcas with farming awareness and an execution delay is investigated. By analyzing the associated characteristic equation, Hopf bifurcation induced by the execution delay is studied for the uncontrolled system. Then, a time-delayed controller is introduced to control the occurrence of Hopf bifurcation. Our study implies that bifurcation dynamics is significantly affected by the change of the fractional order, the feedback gain and the extended feedback delay provided that the other parameters are fixed. A series of numerical simulations is performed, which not only verifies our theoretical results but also reveals some specific features. Numerically, we find that the Hopf bifurcation gradually occurs in advance with the increase of the fractional order, and there exist extreme points for the feedback gain and the extended feedback delay which can minimize the bifurcation value. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
33. Nodal Solutions for Problems with Mean Curvature Operator in Minkowski Space with Nonlinearity Jumping Only at the Origin.
- Author
-
Shen, Wenguo
- Subjects
MINKOWSKI space ,CURVATURE ,HOPF bifurcations ,RADIUS (Geometry) - Abstract
In this paper, we establish a unilateral global bifurcation result for half-linear perturbation problems with mean curvature operator in Minkowski space. As applications of the abovementioned result, we shall prove the existence of nodal solutions for the following problem − div ∇ v / 1 − ∇ v 2 = α x v + + β x v − + λ a x f v , in B R 0 , v x = 0 , on ∂ B R 0 , where λ ≠ 0 is a parameter, R is a positive constant, and B R 0 = x ∈ ℝ N : x < R is the standard open ball in the Euclidean space ℝ N N ≥ 1 which is centered at the origin and has radius R. a(|x|) ∈ C[0, R] is positive, v + = max{ v , 0}, v − = −min{ v , 0}, α(|x|), β(|x|) ∈ C[0, R]; f ∈ C ℝ , ℝ , s f (s) > 0 for s ≠ 0, and f
0 ∈ [0, ∞], where f0 = lim|s|⟶0 f(s)/s. We use unilateral global bifurcation techniques and the approximation of connected components to prove our main results. [ABSTRACT FROM AUTHOR]- Published
- 2020
- Full Text
- View/download PDF
34. Hopf Bifurcation and Dynamic Analysis of an Improved Financial System with Two Delays.
- Author
-
Kai, G., Zhang, W., Jin, Z., and Wang, C. Z.
- Subjects
HOPF bifurcations ,CORPORATE finance ,COMPUTER simulation - Abstract
The complex chaotic dynamics and multistability of financial system are some important problems in micro- and macroeconomic fields. In this paper, we study the influence of two-delay feedback on the nonlinear dynamics behavior of financial system, considering the linear stability of equilibrium point under the condition of single delay and two delays. The system undergoes Hopf bifurcation near the equilibrium point. The stability and bifurcation directions of Hopf bifurcation are studied by using the normal form method and central manifold theory. The theoretical results are verified by numerical simulation. Furthermore, one feature of the proposed financial chaotic system is that its multistability depends extremely on the memristor initial condition and the system parameters. It is shown that the nonlinear dynamics of financial chaotic system can be significantly changed by changing the values of time delays. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
35. Stability and Hopf Bifurcation of Three-Species Prey-Predator System with Time Delays and Allee Effect.
- Author
-
Rihan, F. A., Alsakaji, H. J., and Rajivganthi, C.
- Subjects
ALLEE effect ,TIME delay systems ,HOPF bifurcations ,SYSTEM dynamics ,SENSITIVITY analysis - Abstract
Allee effect is one of the important factors in ecology, and taking it into account can cause significant impacts in the system dynamics. In this paper, we study the dynamics of a two-prey one-predator system, where the growth of both prey populations is subject to Allee effects, and there is a direct competition between the two-prey species having a common predator. Two discrete time delays τ 1 and τ 2 are incorporated into the model to represent reaction time of predators. Sufficient conditions for local stability of positive interior equilibrium and existence of Hopf bifurcations in terms of threshold parameters τ 1 ∗ and τ 2 ∗ are obtained. A Lyapunov functional is deducted to investigate the global stability of positive interior equilibrium. Sensitivity analysis to evaluate the uncertainty of the state variables to small changes in the Allee parameters is also investigated. Presence of Allee effect and time delays in the model increases the complexity of the model and enriches the dynamics of the system. Some numerical simulations are provided to illustrate the effectiveness of the theoretical results. The model is highly sensitive to small changes in Allee parameters at the early stages and with low population densities, and this sensitivity decreases with time. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
36. Hopf Bifurcation and Turing Instability Analysis for the Gierer–Meinhardt Model of the Depletion Type.
- Author
-
Gu, Lianchao, Gong, Peiliang, and Wang, Hongqing
- Subjects
HOPF bifurcations ,HEAT equation ,DIFFUSION coefficients ,BIFURCATION diagrams ,DIFFUSION ,COMPUTER simulation ,LIMIT cycles - Abstract
The reaction diffusion system is one of the important models to describe the objective world. It is of great guiding importance for people to understand the real world by studying the Turing patterns of the reaction diffusion system changing with the system parameters. Therefore, in this paper, we study Gierer–Meinhardt model of the Depletion type which is a representative model in the reaction diffusion system. Firstly, we investigate the stability of the equilibrium and the Hopf bifurcation of the system. The result shows that equilibrium experiences a Hopf bifurcation in certain conditions and the Hopf bifurcation of this system is supercritical. Then, we analyze the system equation with the diffusion and study the impacts of diffusion coefficients on the stability of equilibrium and the limit cycle of system. Finally, we perform the numerical simulations for the obtained results which show that the Turing patterns are either spot or stripe patterns. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
37. Enhancing Ikeda Time Delay System by Breaking the Symmetry of Sine Nonlinearity.
- Author
-
Gao, Xiaojing
- Subjects
LYAPUNOV exponents ,HOPF bifurcations ,LIMIT cycles ,BIFURCATION diagrams ,SYMMETRY - Abstract
In the present contribution, an asymmetric central contraction mutation (ACCM) model is proposed to enhance the Ikeda time delay system. The modified Ikeda system model is designed by introducing a superimposed tanh function term into the sine nonlinearity term. Stability and Hopf bifurcation characteristics of the system are analyzed theoretically. Numerical simulations, carried out in terms of bifurcation diagrams, Lyapunov exponents spectrum, phase portraits, and two-parameter (2D) largest Lyapunov exponent diagrams are employed to highlight the complex dynamical behaviors exhibited by the enhanced system. The results indicate that the modified system has rich dynamical behaviors including limit cycle, multiscroll hyperchaos, chaos, and hyperchaos. Moreover, as a major outcome of this paper, considering the fragile chaos phenomenon, the ACCM-Ikeda time delay system has better dynamical complexity and larger connected chaotic parameter spaces (connectedness means that there is no stripe corresponding to nonchaotic dynamics embedded in the chaos regions). [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
38. Hopf Bifurcation and Control of Magnetic Bearing System with Uncertain Parameter.
- Author
-
Wang, Jing, Ma, Shaojuan, Hao, Peng, and Yuan, Hehui
- Subjects
MAGNETIC control ,UNCERTAIN systems ,MAGNETIC bearings ,MATHEMATICAL analysis ,POLYNOMIAL approximation ,BIFURCATION diagrams ,HOPF bifurcations - Abstract
In this paper, the Hopf bifurcation and control of the magnetic bearing system under an uncertain parameter are investigated. Firstly, the two-degree-of-freedom magnetic bearing system model with uncertain parameter is established. The method of orthogonal polynomial approximation is used to obtain the equivalent magnetic bearing model which is deterministic. Secondly, combining mathematical analysis tools and numerical simulations, the Hopf bifurcation of the equivalent model is analyzed. Finally, a hybrid feedback control method (linear feedback control method combined with nonlinear stochastic feedback control method) is introduced to control the Hopf bifurcation behavior of the magnetic bearing system. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
39. Hopf Bifurcation Analysis of a Synthetic Drug Transmission Model with Time Delays.
- Author
-
Zhang, Zizhen, Yang, Fangfang, and Xia, Wanjun
- Subjects
HOPF bifurcations ,DRUG analysis ,SYNTHETIC drugs ,COMPUTER simulation - Abstract
This paper is concerned with the Hopf bifurcation of a synthetic drug transmission model with two delays. Firstly, some sufficient conditions of delay-induced bifurcation for such a model are captured by using different combinations of the two delays as the bifurcation parameter. Secondly, based on the center manifold theorem and normal form theory, some sufficient conditions determining properties of the Hopf bifurcation such as the direction and the stability are established. Finally, to underline the effectiveness of the obtained results, some numerical simulations are ultimately addressed. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
40. Complex Dynamical Behaviors of a Fractional-Order System Based on a Locally Active Memristor.
- Author
-
Yu, Yajuan, Bao, Han, Shi, Min, Bao, Bocheng, Chen, Yangquan, and Chen, Mo
- Subjects
HYSTERESIS loop ,HOPF bifurcations ,NONLINEAR oscillators ,BEHAVIOR - Abstract
A fractional-order locally active memristor is proposed in this paper. When driven by a bipolar periodic signal, the generated hysteresis loop with two intersections is pinched at the origin. The area of the hysteresis loop changes with the fractional order. Based on the fractional-order locally active memristor, a fractional-order memristive system is constructed. The stability analysis is carried out and the stability conditions for three equilibria are listed. The expression of the fractional order related to Hopf bifurcation is given. The complex dynamical behaviors of Hopf bifurcation, period-doubling bifurcation, bistability and chaos are shown numerically. Furthermore, the bistability behaviors of the different fractional order are validated by the attraction basins in the initial value plane. As an alternative to validating our results, the fractional-order memristive system is implemented by utilizing Simulink of MATLAB. The research results clarify that the complex dynamical behaviors are attributed to two facts: one is the fractional order that affects the stability of the equilibria, and the other is the local activeness of the fractional-order memristor. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
41. A Fractional-Order Model for Zika Virus Infection with Multiple Delays.
- Author
-
Rakkiyappan, R., Latha, V. Preethi, and Rihan, Fathalla A.
- Subjects
ZIKA virus infections ,DELAY differential equations ,FRACTIONAL differential equations ,HOPF bifurcations ,BIOLOGICAL systems - Abstract
Time delays and fractional order play a vital role in biological systems with memory. In this paper, we propose an epidemic model for Zika virus infection using delay differential equations with fractional order. Multiple time delays are incorporated in the model to consider the latency of the infection in a vector and the latency of the infection in the infected host. We investigate the necessary and sufficient conditions for stability of the steady states and Hopf bifurcation with respect to three time delays τ 1 , τ 2 , and τ 3 . The model undergoes a Hopf bifurcation at the threshold parameters τ 1 ∗ , τ 2 ∗ , and τ 3 ∗ . Some numerical simulations are given to show the effectiveness of obtained results. The numerical simulations confirm that combination of fractional order and time delays in the epidemic model effectively enriches the dynamics and strengthens the stability condition of the model. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
42. Bifurcation Analysis of Three-Strategy Imitative Dynamics with Mutations.
- Author
-
Wenjun Hu, Haiyan Tian, and Gang Zhang
- Subjects
HOPF bifurcations ,LIMIT cycles ,BIFURCATION diagrams ,BIOLOGICAL systems ,SOCIAL networks ,COMPUTER simulation - Abstract
Evolutionary game dynamics is an important research, which is widely used in many fields such as social networks, biological systems, and cooperative behaviors. is paper focuses on the Hopf bifurcation in imitative dynamics of three strategies (Rock-Paper-Scissors) with mutations. First, we verify that there is a Hopf bifurcation in the imitative dynamics with no mutation. fien, we find that there is a critical value of mutation such that the system tends to an unstable limit cycle created in a subcritical Hopf bifurcation. Moreover, the Hopf bifurcation exists for other kinds of the considered mutation patterns. Finally, the theoretical results are verified by numerical simulations through Rock-Paper-Scissors game. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
43. Direction and Stability of Hopf Bifurcation in a Delayed Solow Model with Labor Demand.
- Author
-
ElFadily, Sanaa, Kaddar, Abdelilah, and Najib, Khalid
- Subjects
LABOR demand ,HOPF bifurcations ,HAMILTONIAN systems ,POPULATION ,ECONOMIC development ,MANIFOLDS (Mathematics) - Abstract
This paper is concerned with a delayed model of mutual interactions between the economically active population and the economic growth. The main purpose is to investigate the direction and stability of the bifurcating branch resulting from the increase of delay. By using a second order approximation of the center manifold, we compute the first Lyapunov coefficient for Hopf bifurcation points and we show that the system under consideration can undergo a supercritical or subcritical Hopf bifurcation and the bifurcating periodic solution is stable or unstable in a neighborhood of some bifurcation points, depending on the choice of parameters. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
44. Bifurcation Based-Delay Feedback Control Strategy for a Fractional-Order Two-Prey One-Predator System.
- Author
-
Li, Shuai, Huang, Chengdai, and Song, Xinyu
- Subjects
TIME delay systems ,HOPF bifurcations ,FEEDBACK control systems - Abstract
The issue of bifurcation control for a novel fractional-order two-prey and one-predator system with time delay is dealt with in this paper. Firstly, the characteristic equation is investigated by picking time delay as the bifurcation parameter, and some conditions for the appearance of Hopf bifurcation are obtained. It is shown that time delay can give rise to periodic oscillations and each order has an important impact on the occurrence of Hopf bifurcation for the controlled system. Then, it is illustrated that the control result is obviously influenced by the feedback gain. It is also noted that the inception of the bifurcation can be postponed if the feedback gain decreases. Finally, two simulation examples are carried out to verify the chief theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
45. Stability Analysis of a Nonlinear Coupled Vibration Model in a Tandem Cold Rolling Mill.
- Author
-
Lu, Xing, Sun, Jie, Li, Guangtao, Wang, Zhenhua, and Zhang, Dianhua
- Subjects
COLD rolling ,FINITE element method ,HOPF bifurcations ,CONSERVATION laws (Mathematics) ,NONLINEAR dynamical systems - Abstract
Mill chatter in tandem cold rolling mill is a major rejection to the quality and production of the strips. In most mill vibration models, either the roll mass is usually limited to vibrate in vertical direction and vertical-horizontal directions, or the multiple rolls system is simplified to a single mass system. However, the torsional chatter is also a typical type of mill chatter, and the presence of intermediate roll and backup roll will affect the overall vibration of the mill structure system. In this paper, a newly cold rolling mill vibration model coupled with the dynamic rolling processing model and nonlinear vibration model is proposed with the consideration of dynamic coupling and nonlinear characteristics of the rolling process, multiroll equilibrium, and roll movement in both vertical-horizontal-torsional directions. By using Hopf bifurcation theorem and Routh–Hurwitz determinant, the existence of the Hopf bifurcation point of the mill vibration system and bifurcation characteristics are analyzed. At last, the influence of different rolling conditions on the stability of the coupled mill system is investigated, and these results can also be used to design an optimum rolling schedule and determine the appearance of mill chatter under certain rolling conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
46. Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays.
- Author
-
Mbabazi, Fulgensia Kamugisha, Mugisha, Joseph Y. T., and Kimathi, Mark
- Subjects
HOPF bifurcations ,PNEUMOCOCCAL pneumonia ,DELAY differential equations ,TIME delay systems ,STABILITY theory - Abstract
In this paper, a mathematical model of pneumococcal pneumonia with time delays is proposed. The stability theory of delay differential equations is used to analyze the model. The results show that the disease-free equilibrium is asymptotically stable if the control reproduction ratio R
0 is less than unity and unstable otherwise. The stability of equilibria with delays shows that the endemic equilibrium is locally stable without delays and stable if the delays are under conditions. The existence of Hopf-bifurcation is investigated and transversality conditions are proved. The model results suggest that, as the respective delays exceed some critical value past the endemic equilibrium, the system loses stability through the process of local birth or death of oscillations. Further, a decrease or an increase in the delays leads to asymptotic stability or instability of the endemic equilibrium, respectively. The analytical results are supported by numerical simulations. [ABSTRACT FROM AUTHOR]- Published
- 2019
- Full Text
- View/download PDF
47. Hopf Bifurcation and Chaos of a Delayed Finance System.
- Author
-
Zhang, Xuebing and Zhu, Honglan
- Subjects
MATHEMATICAL models of finance ,HOPF bifurcations ,CENTER manifolds (Mathematics) - Abstract
In this paper, a finance system with delay is considered. By analyzing the corresponding characteristic equations, the local stability of equilibrium is established. The existence of Hopf bifurcations at the equilibrium is also discussed. Furthermore, formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theorem. Finally, numerical simulation results are presented to validate the theoretical analysis. Numerical simulation results show that delay can lead a stable system into a chaotic state. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
48. Dynamical Behaviour of a Nutrient-Plankton Model with Holling Type IV, Delay, and Harvesting.
- Author
-
Meng, Xin-You, Wang, Jiao-Guo, and Huo, Hai-Feng
- Subjects
PLANKTON ,TIME delay systems ,PONTRYAGIN'S minimum principle ,HOPF bifurcations ,BIFURCATION theory - Abstract
In this paper, a Holling type IV nutrient-plankton model with time delay and linear plankton harvesting is investigated. The existence and local stability of all equilibria of model without time delay are given. Regarding time delay as bifurcation parameter, such system around the interior equilibrium loses its local stability, and Hopf bifurcation occurs when time delay crosses its critical value. In addition, the properties of the bifurcating periodic solutions are investigated based on normal form theory and center manifold theorem. What is more, the global continuation of the local Hopf bifurcation is discussed by using a global Hopf bifurcation result. Furthermore, the optimal harvesting is obtained by the Pontryagin's Maximum Principle. Finally, some numerical simulations are given to confirm our theoretical analysis. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
49. Stability and Hopf Bifurcation Analysis in a Delayed Myc/E2F/miR-17-92 Network Involving Interlinked Positive and Negative Feedback Loops.
- Author
-
Wang, Guiyuan and Yang, Zhuoqin
- Subjects
STABILITY (Mechanics) ,HOPF bifurcations ,PSYCHOLOGICAL feedback ,BIFURCATION theory ,COMPUTER simulation - Abstract
MiR-17-92 plays an important role in regulating the levels of the Myc/E2F protein. In this paper, we consider a coupling network between Myc/E2F/miR-17-92 delayed negative feedback loop and Myc/E2F positive feedback loop described by a two-dimensional delay differential equation. Based on linear stability analysis and bifurcation theory, sufficient conditions for stability of equilibria and oscillatory behaviors via Hopf bifurcation are derived when choosing time delay as well as negative feedback strength associated with oscillations as bifurcation parameters, respectively. Furthermore, direction and stability of Hopf bifurcation of time delay are studied by using the normal form method and center manifold theorem. Finally, several numerical simulations are performed to verify the results we obtained. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
50. The Gestation Delay: A Factor Causing Complex Dynamics in Gause-Type Competition Models.
- Author
-
Zhang, Zizhen, Upadhyay, Ranjit Kumar, Agrawal, Rashmi, and Datta, Jyotiska
- Subjects
PREDATION ,HOPF bifurcations ,ECOLOGY - Abstract
In this paper, we consider a Gause-type model system consisting of two prey and one predator. Gestation period is considered as the time delay for the conversion of both the prey and predator. Bobcats and their primary prey rabbits and squirrels, found in North America and southern Canada, are taken as an example of an ecological system. It has been observed that there are stability switches and the system becomes unstable due to the effect of time delay. Positive invariance, boundedness, and local stability analysis are studied for the model system. Conditions under which both delayed and nondelayed model systems remain globally stable are found. Criteria which guarantee the persistence of the delayed model system are derived. Conditions for the existence of Hopf bifurcation at the nonzero equilibrium point of the delayed model system are also obtained. Formulae for the direction, stability, and period of the bifurcating solution are conducted using the normal form theory and center manifold theorem. Numerical simulations have been shown to analyze the effect of each of the parameters considered in the formation of the model system on the dynamic behavior of the system. The findings are interesting from the application point of view. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
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