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This paper will explore a fractional-order hepatitis B virus (HBV) infection model that takes into account cell-cell and virus-cell transmission and multiple treatment modalities. The desired control strategy is realized by means of a fractional order PD controller. Firstly, we calculated the basic regeneration number and equilibrium point of the HBV model. Afterwards, for the uncontrolled HBV virus system, the adequate conditions for both stability and Hopf bifurcation are systematically investigated via choosing the appropriate time delay as a parameter for bifurcation. Subsequently, under fractional order PD controller, the effect of a proposed controller on system stability and Hopf bifurcation is studied. The desired dynamic characteristics can be obtained afterwards. Finally, numerical simulations show that all three treatments significantly reduce R 0. The onset of oscillations can be delayed by decreasing the order of the fractional order. There are three control pathways for fractional order PD control, and the generation of bifurcation can also be delayed by changing the gain parameter. Using the above methods, the diffusion of HBV virus particles in the body can be effectively controlled. The conclusions drawn in this paper are extremely novel and have potential theoretical value for the future treatment of hepatitis B illness. [ABSTRACT FROM AUTHOR]

The red palm weevil is one of the most dangerous pests affecting date palm trees in the Gulf region and the Middle East. This paper investigates the control of the red palm weevil (RPW) in date palms using several techniques, namely stem injection, sex pheromone traps, and the Sterile Insect Technique. A mathematical model describing the spread of the red palm weevil is presented, and the boundedness of the solution for the RPW system is studied. The conditions for local stability, forward bifurcation, and Hopf bifurcation are also obtained. Additionally, this research highlights the significance of optimal control in managing RPW and simulates the model using the Forward-Backward Sweep numerical method. It is observed that the parameters of the sterile insect technique, the pheromone trap, and the mechanical injection play important roles in controlling the RPW. Mechanical Injection may be more effective in controlling the palm weevil compared to the other two methods. [ABSTRACT FROM AUTHOR]

There are many harmful effects of smoking. It not only engulfs the health and life of smokers, but also pollutes the air, endangers the life and health of others, and brings a heavy burden to public health. To this end, a delayed smoking model including potential smokers, occasional smokers, smokers, temporary quitters, permanent quitters and smokers with some illness, is investigated in the present paper. Firstly, local stability and existence of Hopf bifurcation of the model is conducted. Secondly, global exponential stability is explored. Lastly, we numerically simulate the correctness of the obtained theoretical results in the paper. [ABSTRACT FROM AUTHOR]

To explore transmission dynamics of tuberculosis, a tuberculosis transmission model with vaccination and time delay is developed in current paper. Positivity and boundedness are analyzed. Local stability of tuberculosis-free equilibrium in respect of the time delay due to latent period of tuberculosis is analyzed and we have found threshold value of the time delay for the local stability of tuberculosis-free equilibrium. Then, local stability of tuberculosis-existence equilibrium following exhibition of Hopf bifurcation at the crucial value of the time delay due to latent period of tuberculosis is derived. It is shown that the developed model undergoes a Hopf bifurcation around the tuberculosis-existence when the time delay due to latent period of tuberculosis passes through the threshold value. Direction and stability of the Hopf bifurcation are investigated with the help of the normal form method and center manifold theory. Finally, numerical simulations are carried out in the justification of obtained analytical findings. The results obtained provide significant information for tuberculosis disease controlling. [ABSTRACT FROM AUTHOR]

This paper examines economic cycles that do not depend on exogenous economic actions. More precisely, the paper develops a positive model of government behavior in order to define the intertemporal fiscal policies that are optimal for a country and which, determine both the optimal budget level and the optimal level of environmental quality. For this purpose, we establish an optimal control model involving intertemporal subsidy strategies characteristically used by an authoritarian government similar to those found in central Europe. It will be shown that by applying the Hopf bifurcation theorem,a cyclical strategy – that is, waves of regulation, environmental subsidies alternating with deregulation and cuts in social programs – may represent an optimal policy. In this paper, we propose an extremely simple optimal control model which is applied to budget surpluses and environmental subsidies. We investigate the cyclical environmental policies as applied through the bifurcation theorem. A number of propositions are stated during the solution process. The first proposition sets the rules in the model parameters in order to establish the cyclical policies. A second proposition sets the relationship between the discount rate and the opportunity cost of capital, which is used to determine a taxing strategy which becomes the future optimal subsidy policy. [ABSTRACT FROM AUTHOR]

Abstract This paper shows the importance of considering the thermal state of a combustor to investigate or predict its thermoacoustic stability. This aspect is often neglected or regarded as less important than the effect of the operating parameters, such as thermal power or equivalence ratio, but under certain circumstances it can have a dramatic influence on the development of the instabilities. The paper presents experimental results collected from a combustor featuring a lean swirl-stabilized flame exhibiting thermoacoustic instability at some operating conditions. It is shown that this instability is caused by a change of the flame topology that is induced by the progressive increase of the wall temperature with the thermal power. This dependence of the instability on wall temperature leads to inertial effects and hysteresis when the operating condition is changed dynamically. A low-order model of the system reproducing this remarkable dynamics is proposed and validated against the experimental data. [ABSTRACT FROM AUTHOR]

Gene regulatory networks play an extremely important role in human life activities. This paper presents a novel fractional-order gene regulatory network model (NFGRNM). The model employs incommensurate fractional orders and introduces time delay arising from the binding of miRNAs to RNA. Time delay often triggers instability such as oscillation and bifurcation, so in this paper we introduce a generalized hybrid control to control the unstable dynamical behavior induced by time delay. First we derive the NFGRNM using fractional order theory, after which the equilibrium point of the network model is calculated. Next, a systematic dynamics analysis of the NFGRNM is performed to derive sufficient conditions to generate the Hopf bifurcation. Most importantly, we introduce the extended hybrid control for the periodic oscillations generated by the time delay in the NFGRNM. Finally, numerical simulation results show that the order of the fractional order can have a great impact on the dynamical behavior of the network model and that the hybrid control has a significant role in delaying (or advancing) the Hopf bifurcation. Since infectious diseases such as SARS-Cov-2, influenza A, and HIV are still prevalent today, the study of gene regulatory networks not only promotes the study of the dynamics of complex networks but also has profound implications for the study of virus transmission in the host and various life activities in humans. • The time lag generated by miRNA-RNA binding is used as a bifurcation parameter. • The Hopf bifurcation behavior of gene regulatory network models is investigated and generalized hybrid control is added. • The effect of fractional order and control parameters on the robustness of the system is investigated. • The effect of disproportionate fractional orders and control parameters on the dynamical behavior of system bifurcations. [ABSTRACT FROM AUTHOR]

Time-delay effect and bifurcation phenomenon are important topics in the study of reaction–diffusion equations. In this paper, we consider a three-species predator–prey system with diffusion and incubation delay for predator. The stability and Hopf bifurcation are mainly discussed. We conclude that there exists a critical value of delay, such that the internal equilibrium is stable or unstable as the delay crosses the critical value. Especially, the system emerges Hopf bifurcation phenomenon at this critical value. For bifurcation solution, the conclusions of stability, period and bifurcation direction are also presented. Additionally, numerical simulations are proceeded to support the main results. In biology, the existence of bifurcation solution means that when the delay of predator reaches to a certain extent, the predator and prey will coexist within a period of time. It turns out that the related computations and analyses are much more complicated than that of two-species time-delay systems. • A predation model with time-delay and diffusion is considered. • Results on stability and Hopf-bifurcations are obtained. • Hopf-bifurcation graphs are performed to illustrate the theoretical analysis. • It is found that time-delay has significant impacts on the pattern formations. [ABSTRACT FROM AUTHOR]

This paper is concerned with the Hopf bifurcation of a delayed SEIQR (Susceptible-Exposed-Infectious- Quarantined-Recovered) worm propagation model in mobile internet. Firstly, a distinct set of conditions that ensures existence of the Hopf bifurcation are derived by analyzing the roots of the associated characteristic equation and regarding the delay as a bifurcation parameter. Secondly, the normal form theory and the center manifold theorem are employed to determine direction of the Hopf bifurcation and stability of the bifurcating periodic solutions. Finally, some numerical simulations are presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the Hopf bifurcation of a delayed SEIQR (Susceptible-Exposed-Infectious- Quarantined-Recovered) worm propagation model in mobile internet. Firstly, a distinct set of conditions that ensures existence of the Hopf bifurcation are derived by analyzing the roots of the associated characteristic equation and regarding the delay as a bifurcation parameter. Secondly, the normal form theory and the center manifold theorem are employed to determine direction of the Hopf bifurcation and stability of the bifurcating periodic solutions. Finally, some numerical simulations are presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper proposes a delayed feedback control strategy for a fractional ecological infectious disease system with infected predators. Firstly, for the uncontrolled system, the stability of each equilibrium is discussed. Choosing the gestational delay as the branching parameter, the conditions of Hopf bifurcation are given at the positive equilibrium. The results show that the stable domain for the fractional system is larger than that for the integer-order system. Secondly, for the controlled system, the effects of gestational delay and feedback delay on the induction of the Hopf bifurcation are investigated, respectively. In addition, we find that the feedback gain coefficient also changes the critical value at which Hopf bifurcation occurs. Selecting a suitable feedback controller can effectively extend the stable domain of the system compared to the control-free system. Finally, the accuracy and effectiveness of the delay feedback controller in controlling the bifurcation are verified through numerical simulations. • A new fractional ecological model with a delay feedback controller is proposed. • Impact of gestational delay and feedback delay on Hopf bifurcation was investigated. • A new control strategy is used to enhance the stability of the fractional system. [ABSTRACT FROM AUTHOR]

In this paper, an autonomous three-dimensional Helmholtz-type oscillator is designed based on conversion of an autonomous Helmholtz two-dimensional oscillator to a jerk oscillator. For a suitable choice of the parameters, the proposed autonomous Helmholtz jerk oscillator can generate Hopf bifurcation, bistable period-2 limit cycles, two types of one-scroll chaotic attractors and coexistence between period-3 limit cycle and one-scroll chaotic attractors. Using a weak modulation of a parameter of the proposed Helmholtz jerk oscillator, it is possible to destroy the coexisting attractors found and transform the proposed Helmholtz jerk oscillator to period-3 oscillations. Moreover using experiments and OrCAD-PSpice software, circuit implementation of the proposed autonomous Helmholtz jerk oscillator is realized in order to check the one-scroll chaotic attractors and the coexisting attractors found during the numerical simulations. Numerical and experimental/OrCAD-PSpice results have a good qualitative agreement. Finally, by adding two new parameters in the proposed autonomous Helmholtz jerk oscillator, it is possible to control the amplitude of the attractor and the largest Lyapunov exponent. [ABSTRACT FROM AUTHOR]

In this paper, an autonomous Toda jerk oscillator is proposed and analysed. The autonomous Toda jerk oscillator is obtained by converting an autonomous two-dimensional Toda oscillator with an exponential nonlinear term to a jerk oscillator. The existence of Hopf bifurcation is established during the stability analysis of the unique equilibrium point. For a suitable choice of the parameters, the proposed autonomous Toda jerk oscillator can generate antimonotonicity, periodic oscillations, chaotic oscillations and bubbles. By introducing two additional parameters in the proposed autonomous Toda jerk oscillator, it is possible to control partially or totally the amplitude of its signals. In addition, electronic circuit realization of the proposed Toda jerk oscillator is carried out to confirm results found during numerical simulations. The commensurate fractional-order version of the proposed autonomous chaotic Toda jerk oscillator is studied using the stability theorem of fractional-order oscillators and numerical simulations. It is found that periodic oscillations and chaos exist in the fractional-order form of the proposed Toda jerk oscillator with order less than three. Finally, combination synchronization of two fractional-order proposed autonomous chaotic Toda jerk oscillators with another fractional-order proposed autonomous chaotic Toda jerk oscillator is analysed using the nonlinear feedback control method. [ABSTRACT FROM AUTHOR]

Oscillatory behavior is a ubiquitous phenomenon in various physical and biological processes. Recently, it has been reported that oscillations of wireless sensor networks infected by virus (WSNIVs) can potentially be deleterious to the security strength of systems and may even cause network congestion and paralysis. Moreover, it has been discovered that latency delays are essential for the function of WSNIVs and can drive instability and periodic oscillations, enhance complexity, and even lead to multistability and chaotic motion. However, the precise roles of such delay during the regulation process are still not completely understood. Here, the primary objective of this paper is to study oscillatory behaviors of WSNIVs with latency delay. In particular, the sufficient conditions for local stability and existence with Hopf bifurcation are obtained. Moreover, we further discuss the properties of Hopf bifurcation by using the normal form and the center manifold theorem. The obtained results show that the latency delay can drive the WSNIVs to be oscillatory even when the network is at a stable state, suggesting that such delay might be a potential hazard to the security of wireless sensor systems. Our findings highlight the importance of considering delays when developing safer and more effective wireless sensor networks. Finally, we test and analyze the above research results through numerical calculation with Matlab and simulation experiments with OPNET, and the conclusions are verified to be correct and effective in experiments. [ABSTRACT FROM AUTHOR]

Highlights • Model of mosaic disease of Jatropha curcas plants is proposed. • Effects of awareness-based use of nutrients and insecticides are investigated. • Awareness based on observation of infection cannot lead to eradication of disease. • Global awareness campaigns can eradicate the disease if the transmission is weak. Abstract Plant diseases are responsible for substantial and sometimes devastating economic and societal costs and thus are a major limiting factor for stable and sustainable agricultural production. Diseases of crops are particular crippling in developing countries that are heavily dependent on agriculture for food security and income. Various techniques have been developed to reduce the negative impact of plant diseases and eliminate the associated parasites, but the success of these approaches strongly depends on population awareness and the degree of engagement with disease control and prevention programs. In this paper we derive and analyse a mathematical model of mosaic disease of Jatropha curcas , an important biofuel plant, with particular emphasis on the effects of interventions in the form of nutrients and insecticides, whose use depends on the level of population awareness. Two contributions to disease awareness are considered in the model: global awareness campaigns, and awareness from observing infected plants. All steady states of the model are found, and their stability is analysed in terms of system parameters. We identify parameter regions associated with eradication of disease, stable endemic infection, and periodic oscillations in the level of infection. Analytical results are supported by numerical simulations that illustrate the behaviour of the model in different dynamical regimes. Implications of theoretical results for practical implementation of disease control are discussed. [ABSTRACT FROM AUTHOR]

In this paper, the variable order fractional permanent magnet synchronous motor (VOFPMSM) is investigated. Conditions for existence and uniqueness of the solution of the VOFPMSM are proposed. The stability behavior of the system's equilibrium points along with the variation of the motor parameters and the order of differentiation is discussed. Sufficient conditions that guarantee the asymptotic stability of each of the equilibrium points of the system are established. Also, the required conditions that give the effect of Hopf bifurcation of the system are established in terms of the system parameters and the order of differentiation and consequently the appearance of the chaotic behavior of the VOFPMSM. New numerical techniques based on the modified backward Euler's schemes for continuous and discontinuous variable order fractional model are presented. The obtained numerical results demonstrate the merits of the proposed method and the variable order fractional permanent magnet synchronous motor over the fractional permanent magnet synchronous motor. [ABSTRACT FROM AUTHOR]

In this paper, in view of the senescence of plant and the decay of wrack, time delays are introduced into the plant-wrack model. The effects of wrack decay and time delay on the dynamical behaviors of the diffusive plant-wrack model are studied analytically and numerically. When the delay is zero, the wrack decay will induce the change of stability of the unique equilibrium point, further lead to the occurrence of the Hopf bifurcation and the Turing instability. When the delay is present, the conditions for the occurrence of the Hopf bifurcation are established. By comparing the results of the model without and with delay, it is found that the increases of delay may induce no stability switches, a single stability switch or multiple stability switches, when the value of wrack decay can stabilize model with zero delay. When the value of wrack decay can destabilize model with zero delay, numerical simulations show that the small delay may cause homogeneous distributions of vegetation, while the larger delay may cause the emergence of periodic oscillation of vegetation. The obtained results provide a basis for understanding the spatiotemporal evolution of such a plant-wrack model with delay. • Plant-wrack model with delay is proposed. • Effects of wrack decay and delay are analyzed. • Complex dynamics are presented. [ABSTRACT FROM AUTHOR]

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In present paper, a delayed SEIR model of malware propagation on mobile wireless sensor networks is formulated. Basic reproduction number of the model is calculated by employing the next generation matrix method and impact of the time delay due to incubation period of malware is discussed with the help of eigenvalue method. What is more, properties of the Hopf bifurcation are derived by using center manifold method. To minimize number of the infectious nodes and the cost related with detoxication, an optimal control strategy is presented by constructing a suitable Hamiltonian function. Numerical calculations are performed to justify the obtained theoretical findings. • A delayed SEIR model of malware propagation on mobile wireless sensor networks is formulated. • Existence and properties of Hopf bifurcation of the model are analyzed. • Optimal control of the model is solved. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to continue the investigations of the important system of Fengqi et al. (2008). The occurrence of Turing and Hopf bifurcations in small homogeneous arrays of two coupled reactors via diffusion-linked mass transfer which described by a system of ordinary differential equations is considered. I study the conditions of the existence as well as stability properties of the equilibrium solutions and derive the precise conditions on the parameters to show that the Hopf bifurcation occurs. Analytically I show that a diffusion driven instability occurs at a certain critical value, when the system undergoes a Turing bifurcation, patterns emerge. The spatially homogeneous equilibrium loses its stability and two new spatially non-constant stable equilibria emerge which are asymptotically stable. Numerically, at a certain critical value of diffusion the periodic solution gets destabilized and two new spatially nonconstant periodic solutions arise by Turing bifurcation. [ABSTRACT FROM AUTHOR]

In current paper, a delayed SEI 2 RS malware dissemination model in cyber–physical systems is proposed. Effect of the time delay owning to temporary immunity interval of the recovered nodes is analyzed. A series of sufficient criteria determining local stability of malware-existence equilibrium and occurrence of Hopf bifurcation are revealed via regarding the time delay owning to temporary immunity interval of the recovered nodes as bifurcation parameter. Additionally, direction and stability of the Hopf bifurcation are explored with the aid of the center manifold theorem and normal form theory method. At last, numerical calculations are conducted to prove validity of obtained results. • A delayed SEI2RS malware dissemination model in cyber–physical systems is proposed. • Impact of the time delay on the model is analyzed. • Properties of Hopf bifurcation are investigated. • Some suggestions for controlling malware dissemination in cyber–physical systems are presented. [ABSTRACT FROM AUTHOR]

This paper formulates a Susceptible–Latent–Breaking out–Patched–Susceptible (SLBPS) virus propagation model with delay of temporary immunity. The influence of time delay on stability of the model is examined by analyzing the distribution of eigenvalues of the characteristic equation. Furthermore, we also demonstrate the direction and stability of the Hopf bifurcation. Lastly, optimal control strategies in terms of the rate at which susceptible, latent, break out nodes acquiring patches to improve performance of the model are presented. For the sake of the correctness of the theoretical analysis, some numerical simulations are also presented. • A delayed SLBPS virus-patch model. • Existence and properties of Hopf bifurcation of are analyzed. • Optimal control of the model is solved. [ABSTRACT FROM AUTHOR]

Malware such as virus, worm, and Trojan horse, is a software designed to pose harmful and undesirable effects on communication networks. It can cause numerous sever damage like data loss , repeated occupation of the memory space and corrupting databases etc. To overcome such and other related drastic threats, we need to fight against and control spread of malware at large scale. For this goal, a delayed e-epidemic SEIRS malware propagation model with a generalized non-monotone incidence rate is formulated in our paper. The basic reproduction number is derived. Then local stability and Hopf bifurcation analysis of the viral equilibrium is performed. Further, properties of the Hopf bifurcation are carried out. Finally, numerical simulations are implemented to justify the theoretical findings. • A study of Malware such as virus, worm, and Trojan horse and their undesirable effects on communication networks. • A delayed epidemic SEIRS malware propagation model with a generalized non-monotone incidence rate is formulated. • Local stability and Hopf bifurcation analysis of the viral equilibrium is performed. [ABSTRACT FROM AUTHOR]

This paper discusses the role of investment on dynamics of micro-economic in non-linear financial model with distributed time delay feedback and effect of delay on the dynamics of micro-economic in nonlinear financial model with distributed time delay feedback. The interest rate, investment demand and price index are modelled with the help of saving amount, cost per investment, demand elasticity of commercial markets and the strength of feedback. All these parameters are considered as positive. Using bifurcation theory, bifurcation point and time period are studied for the financial system with distributed time delay feedback. Through numerical methods, it is observed that the value of time bifurcation with time delay feedback in investment increases as investment demand increases, further the time bifurcation increases with the investment demand parameter and strength of time delay feedback in investment demand. It is concluded that the bifurcation analysis depends on the value of investment demand and also on the strength of time delay feedback parameter. [ABSTRACT FROM AUTHOR]

In this paper, a coupled FitzHugh–Nagumo (FHN) neural system with time delay has been proposed and its stability and Hopf bifurcation are researched. Specifically, the stability of equilibrium point is analyzed by employing the corresponding characteristic equation. Sufficient conditions for existence of Hopf bifurcation are obtained. The results show that the FHN neural system exhibits the parameter regions involved the delay-independence stability and delay dependence stability. Increase of time delay can induce the stability switches between resting state and periodic activity. Furthermore, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out for illustrating the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper the linear stability of the delayed logistic equation with additive Allee effect is investigated. We also analyze the associated characteristic transcendental equation, to show the occurrence of Hopf bifurcation at the positive equilibrium. To determine the direction of Hopf bifurcation and the stability of bifurcating periodic solution, we use the normal form approach and a center manifold theorem. Finally, a numerical example is given to demonstrate the effectiveness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

The energy storage devices incorporated into FACTS controllers increase the operational flexibility and reduce capital cost. This paper investigates the effect of Static Synchronous Compensator with energy storage (STATCOM-ES) on dynamic bifurcations of Subsynchronous resonance (SSR). The test system considered is IEEE first benchmark model (FBM). The line is provided with fixed series compensation and active shunt compensation at the electrical center of the line. The degree of series compensation is taken as the bifurcation parameter. The results of bifurcation analysis are validated by performing transient simulation of the system. [ABSTRACT FROM AUTHOR]

In this paper, bifurcation analysis is performed on a two-level twelve-pulse voltage source converter (VSC) based STATCOM to study the impact of dc capacitor on stabilty of the system. STATCOM is modeled in D-Q frame with the reactive current controller. The non-linear feedback controller is designed to control the bifurcation of the STATCOM in the inductive region to eliminate the Hopf bifurcations and limiting point cycles. The results obtained using bifurcation analysis is validated by eigen value analysis and transient simulations. [ABSTRACT FROM AUTHOR]

In this paper, dynamical behaviors including stability and Hopf bifurcation of a delayed SIR epidemic model with convex incidence rate are examined. We first discuss the existence of Hopf bifurcation. Subsequently, direction and stability of Hopf bifurcation are investigated. Moreover, length of the time delay which can retain stability of the proposed model has been appraised. Specially, global exponential stability is studied. Finally, numerical simulations are carried out with the suitable choices of parameters in the prosed model. [ABSTRACT FROM AUTHOR]

In this paper, a ratio dependent delayed predator-prey model with Holling-Tanner type functional response is studied. The local stability of a positive equilibrium and the existence of Hopf bifurcations are established. By using the normal form theory and center manifold theorem, the explicit algorithm determining the stability, direction of the bifurcating periodic solutions are derived. Finally, numerical simulations for justifying the theoretical analysis are also presented. [ABSTRACT FROM AUTHOR]

In this paper, a ratio dependent delayed predator-prey model with Holling-Tanner type functional response is studied. The local stability of a positive equilibrium and the existence of Hopf bifurcations are established. By using the normal form theory and center manifold theorem, the explicit algorithm determining the stability, direction of the bifurcating periodic solutions are derived. Finally, numerical simulations for justifying the theoretical analysis are also presented. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents an investigation on bifurcation of railway bogie behavior in the presence of nonlinearities which are yaw damping forces in longitudinal suspension system and the friction creepage model of the wheel/rail contact including clearance. Through Routh–Hurwitz stability criterion and a more accurate model than Yang and Ahmadian, the analytical expression of critical speed is achieved as well as the limit cycle frequency. Then, by Averaging method and analytical critical speed, the amplitude of the limit cycle is determined while the wheel/rail clearance is taken into account. To solve the nonlinear equations analytically, both dead zone discontinuity and yaw dampers must be formulated properly. In this direction, a suitable and novel exact equivalent functions (EF) is introduced. Furthermore, 2D and 3D bifurcation diagrams are depicted to show the mechanism creation of Hopf bifurcation which is employed in the design of stable wheelset systems. Finally, the accuracy of one-axle model results for the prediction of critical speed is evaluated in contrast with two-axle bogie model. [Copyright &y& Elsevier]

This paper deals with the bifurcations of non-semi-simple eigenvalues at critical point of Hopf bifurcation to understand the dynamic behavior of the system. By using the Puiseux expansion, the expression of the bifurcation of non-semi-simple eigenvalues and the corresponding topological structure in the parameter space are obtained. The zero-order approximate solutions in the vicinity of the critical points at which the multiple Hopf bifurcation may occur are developed. A numerical example, the flutter problem of an airfoil in simplified model, is given to illustrate the application of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we analyze the dynamical behaviour of a bioeconomic model system using differential algebraic equations. The system describes a prey–predator fishery with prey dispersal in a two-patch environment, one of which is a free fishing zone and other is a protected zone. It is observed that a singularity-induced bifurcation phenomenon appears when a variation of the economic interest of harvesting is taken into account. We have incorporated a state feedback controller to stabilize the model system in the case of positive economic interest. A discrete-type gestational delay of predators is incorporated, and its effect on the dynamical behaviour of the model is analyzed. The occurrence of Hopf bifurcation of the proposed model with positive economic profit is shown in the neighbourhood of the coexisting equilibrium point through considering the delay as a bifurcation parameter. Finally, some numerical simulations are given to verify the analytical results, and the system is analyzed through graphical illustrations. [Copyright &y& Elsevier]

In order to maintain the harmony and stability of ecosystems, in this paper, the stability of Nicholson's blowflies model with time delay was investigated. The distribution of the characteristic roots, the stability of the equilibrium, the existence of Hopf bifurcation and its conditions were discussed. Meanwhile, some simulations were carried out, which supported the theoretical results obtained previously and the global existence of Hopf bifurcation near the positive equilibrium point was got. At last, the reasons of circulating ecosystems were explained by the bifurcation theory. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the dynamical behavior of an eco-epidemiological model with distributed delay is studied. Sufficient conditions for the asymptotical stability of all the equilibria are obtained. We prove that there exists a threshold value of the conversion rate beyond which the positive equilibrium bifurcates towards a periodic solution. We further analyze the orbital stability of the periodic orbits arising from bifurcation by applying Poore’s condition. Numerical simulation with some hypothetical sets of data has been done to support the analytical findings. [Copyright &y& Elsevier]

In this paper we develop an invasive species differential equations model for the population collapse on Easter Island. This model, motivated by recent archaeological results of T. Hunt, allows us to examine the role of rats in the collapse. In Hunt's theory, the decline of resources was accelerated by Polynesian rats and not merely the result of the overuse by the island's human population. Hunt uses archaeological data which suggests a different timeline for the settlement and the long term population dynamics of Easter Island. Our goal is to estimate the plausibility of Hunt's hypothesis. [ABSTRACT FROM AUTHOR]

A nonlinear model of hydraulic turbine governing systems with elastic water hammer effect is presented. Based on the model, in the cases of frequency disturbance, load disturbance and without disturbance, bifurcation theories of dynamical systems are applied to analyze the Hopf bifurcation phenomena in the systems with the change of PID regulator parameters. The critical points of Hopf bifurcation, stable regions and bifurcation diagrams are obtained in the PID parameter spaces. The results are in comparison with those of non-elastic water hammer effect. In conclusion, with the varieties of PID parameters, the unexpected and sustained oscillation may appear in hydraulic turbine governing systems. For the sake of safety and stability, the regulator parameters should be set in the stable regions of parameter spaces. The simulations verify the results of the paper. [ABSTRACT FROM AUTHOR]

Most of the infectious diseases associated with human population are still a threat to become epidemic in the globe. Mathematical models have been an important tool to study the complex behavior of infectious diseases. In this paper a deterministic SVIRS epidemic model with Holling type II incidence rate and treatment rate including three delays is investigated. Local stability of disease equilibrium and existence of Hopf bifurcation are discussed explicitly. Then, direction and stability of the bifurcated periodic solutions are determined. Finally, with the suitable choices of the parameters, numerical simulations are presented in order to verify effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

Computer virus has caused terrible damage. Establishing appropriate mathematical model is beneficial for comprehending the propagation regular pattern of computer virus. So, in this paper, we build a new Susceptible-Exposed-Infected-Kill signals-Recovered (SEIR-KS) computer virus model with two delays. At first, we obtain the basic regeneration number. Afterwards, we regard time delays as parameters and investigate the local stability and Hopf bifurcation of the endemic equilibrium by discussing the distribution of the eigenvalues of the corresponding characteristic equation. Then, we research direction and stability of Hopf bifurcation. In addition, we take some numerical simulations by Matlab to validate the correctness of theoretical results. At last, we analyze the basic reproductive rate and put forward some scientific advices. [ABSTRACT FROM AUTHOR]

A critical evaluation of current hydraulic servo system analysis methods indicates a need for alternative methods better able to quantify robust stability. One promising method recently developed for analysing large-scale power systems determines stability robustness in a high-dimensional parameter space by computing the distance to the `closest' Hopf bifurcation (which corresponds to the birth of a limit cycle oscillation). In this paper a procedure is developed for applying closest Hopf bifurcation theory in the design and analysis of robustly stable hydraulic servo systems. The procedure addresses practical implementation issues such as the impact of an inhomogeneous parameter space and the choice of a metric that yields a meaningful quantitative measure of stability robustness. Results from the new procedure applied to a common position control system compare favourably with published describing function results and new simulation results. Additionally, the new procedure is easier to apply and produces results which are easier to interpret and use. As a demonstration of the design procedure's ability to handle non-linear systems with high-dimensional parameter spaces, a hydraulic servo system with an inhomogeneous seven-dimensional parameter space is designed to meet a robust stability requirement. [ABSTRACT FROM AUTHOR]

A delayed SEIRS worm propagation model with the inclusion of a finite communication radius and node density for wireless sensor networks is investigated in this paper. By using different combinations of the three delays as bifurcating parameter and analyzing distribution of roots of the corresponding characteristic equation, sufficient conditions are derived for local stability of the endemic equilibrium and the existence of a Hopf bifurcation at the endemic equilibrium are addressed. By constructing a suitable Lyapunov function, sufficient conditions for global stability of the endemic equilibrium are determined. Finally, numerical simulations for a set of parameter values are performed to illustrate the analytical findings. [ABSTRACT FROM AUTHOR]