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The sterile insect technique (SIT) has been applied as an alternative method to reduce or eradicate mosquito-borne diseases. To explore the impact of the sterile mosquitoes on controlling the wild mosquito populations, in this paper, we further extend the work in [J. Li, New revised simple models for interactive wild and sterile mosquito populations and their dynamics, J. Biol. Dyn. 11(S2) (2017) 316–333] and formulate delayed models for interactive wild and sterile mosquitoes, which can depict wild mosquito population undergoing distinct stages of development during a lifetime. By performing mathematical analysis, the threshold dynamics of the proposed models are explored, respectively. In particular, Hopf bifurcation phenomena are observed as the delay τ is varying. Numerical examples illustrate our findings. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of bifurcation analysis and bifurcation control of a fractional-order gene regulatory network with sRNA. Firstly, the process of stability change of system equilibrium under the influence of the sum of time delay is discussed, the critical condition of Hopf bifurcation is explored, and the effect of fractional order on the system stability domain. Secondly, aiming at the system's instability caused by a large time delay, we design a controller to improve the system's stability and derive the parameter conditions that satisfy the system's stability. It is found that changing the parameter values of the controller within a certain range can control the system's nonlinear behaviours and effectively expand the stability range. Then, a numerical example is given to illustrate the results of this paper. [ABSTRACT FROM AUTHOR]

The security of mobile wireless sensor networks has captivated extensive attention of researchers because of their wide range of applications and vulnerability to attacks caused by malware. In this paper, we investigate a delayed malware propagation model on mobile wireless sensor network incorporating nonlinear incidence rate, logistic growth rate and recovery rate. Local asymptotic stability of the endemic equilibrium and existence of Hopf bifurcation at crucial value of the time delay are analyzed. Then, properties of Hopf bifurcation are explored. Specifically, global exponential stability is investigated via linear matrix inequality. An example is presented finally to underline the effectiveness of findings in our paper numerically and graphically. [ABSTRACT FROM AUTHOR]

This paper explores a predator–prey system featuring fear and disease within the predator population,utilizing the Rosenzweig–MacArthur model with Holling type-II functional response. The primary focus lies in investigating the impact of a fear factor, wherein the prey's growth rate is hindered due to predator-induced fear. Additionally, the model accounts for the spread of disease among predators,leading to a division between susceptible and infected predator subpopulations. The inclusion of an Allee effect in the susceptible predator further enriches the model. The study involves a thorough examination, encompassing local and global stability analysis as well as Hopf bifurcation analysis around the interior equilibrium point. Numerical simulations underscore a noteworthy observation: an escalation in interaction force propels the system into chaotic dynamics,marked by stable focus, limit cycles and period-doubling phenomena. A noteworthy finding pertains to the influence of the Allee parameter (θ) on chaotic dynamics. As the Allee parameter values increase, the system tends to stable focus through a sequence of chaotic states, period-doubling and limit cycles. Subsequently, the paper introduces the role of another pivotal parameter, the fear factor, into the chaotic dynamics. Intriguingly, chaos transforms into stable focus through diverse nonlinear phenomena, including period-doubling and limit cycles. This nuanced exploration of parameters sheds light on the intricate dynamics governing the predator–prey system, offering a comprehensive understanding of the interplay between fear, disease and ecological factors. So our observation throughout this paper that how chaos behaves here after one by one injection of our new features: fear factor and Allee parameter? [ABSTRACT FROM AUTHOR]

A double-time-delay Holling Ⅱ predator model with weak Allee effect and age structure was studied in this paper. First, the model was converted into an abstract Cauchy problem. We also discussed the well-posedness of the model and the existence of the equilibrium solution. We analyzed the global stability of boundary equilibrium points, the local stability of positive equilibrium points, and the conditions of the Hopf bifurcation for the system. The conclusion was verified by numerical simulation. [ABSTRACT FROM AUTHOR]

In this paper, we propose a diffusive predator–prey model with two delays, i.e., a spatial memory delay and a toxic effect delay. Initially, we analyze the global existence of the solution of the system. We then analyze the equilibria’s local stability without delays and investigate the Hopf bifurcation induced by one delay. Subsequently, we establish an analytical framework for constructing the stability switching curve in the delay space. Finally, we present numerical simulations to validate the theoretical results and verify the emergence of various spatial patterns in the system. [ABSTRACT FROM AUTHOR]

In this paper, we formulate a diffusive prey–predator system with strong Allee effect in prey, spatial memory, and gestation delay of predator. Turing instability and Hopf bifurcation are investigated extensively. The system more easily creates Turing patterns, when the predator owns sluggish memory-induced diffusion. If the predator owns rapid memory-induced diffusion, then the system may present abundant dynamics. Predator with long memory displays a spatial nonhomogeneous periodic spread once the system only contains spatial memory delay. Populations are in a homogeneous or nonhomogeneous periodic spread with gestation period. However, under the combined influences of memory delay and gestation delay, the stability switches appear. Strong Allee effect has obvious influences on the system. The positive equilibrium is linearly stable if there is no strong Allee effect; once strong Allee effect is reasonable, it is unstable. But if the Allee effect is huge enough, then two populations can die out. Finally, we investigate the results by numerical simulations, which demonstrate that spatial memory, gestation delay, and strong Allee effect are conductive to the dynamics of the system. [ABSTRACT FROM AUTHOR]

In this paper, we consider the long-term sustainability of the northeast Korean pine. We propose a class of natural Korean pine population system with time delay and diffusion term. First, by analyzing the roots distribution of the characteristic equation, we study the stability of the model system with diffusion terms and prove the occurrence of Hopf bifurcation. Second, we introduce lactation time delay into a population model with a diffusion term, based on stability theory of ordinary differential equation, norm form methods and center manifold theorem, the stability of bifurcating periodic solutions and the relevant formula for the direction of Hopf bifurcation are given. Finally, some numerical simulations are given. [ABSTRACT FROM AUTHOR]

The spread of infectious diseases often presents the emergent properties, which leads to more difficulties in prevention and treatment. In this paper, the SIR model with both delay and network is investigated to show the emergent properties of the infectious diseases' spread. The stability of the SIR model with a delay and two delay is analyzed to illustrate the effect of delay on the periodic outbreak of the epidemic. Then the stability conditions of Hopf bifurcation are derived by using central manifold to obtain the direction of bifurcation, which is vital for the generation of emergent behavior. Also, numerical simulation shows that the connection probability can affect the types of the spatio-temporal patterns, further induces the emergent properties. Finally, the emergent properties of COVID-19 are explained by the above results. [ABSTRACT FROM AUTHOR]

This paper proposes a fractional-order reserve biological prey-predator system with a practical specimen biological system incorporating a mixed functional response and fear effect on prey populace because of predation. The fractional-order system describes using the Holling type I and III functional responses. The existence, non-negativity, uniqueness, and boundedness of the solutions along with the local asymptotic stability of the equilibrium points, are investigated from a mathematical point of view. For the reserve biological fractional-order prey-predator system, we have investigated how the fear effect interacts with fractional influencing the local stability and Hopf bifurcation of the system. In this instance, the prerequisites for the fractional-order model’s stability and the occurrence of Hopf bifurcation are illustrated. Numerical examples are exhibited to approve the hypothetical outcomes of the fractional-order prey-predator system. [ABSTRACT FROM AUTHOR]

In this paper, the stability and bifurcation of a two–dimensional p53 gene regulatory network without and with time delay are taken into account by rigorous theoretical analyses and numerical simulations. In the absence of time delay, the existence and local stability of the positive equilibrium are considered through the Descartes' rule of signs, the determinant and trace of the Jacobian matrix, respectively. Then, the conditions for the occurrence of codimension–1 saddle–node and Hopf bifurcation are obtained with the help of Sotomayor's theorem and the Hopf bifurcation theorem, respectively, and the stability of the limit cycle induced by hopf bifurcation is analyzed through the calculation of the first Lyapunov number. Furthermore, codimension-2 Bogdanov–Takens bifurcation is investigated by calculating a universal unfolding near the cusp. In the presence of time delay, we prove that time delay can destabilize a stable equilibrium. All theoretical analyses are supported by numerical simulations. These results will expand our understanding of the complex dynamics of p53 and provide several potential biological applications. [ABSTRACT FROM AUTHOR]

In this paper, we study a diffusive predator–prey model with hyperbolic mortality and prey-taxis under homogeneous Neumann boundary condition. We first analyze the influence of prey-taxis on the local stability of constant equilibria. It turns out that prey-taxis has influence on the stability of the unique positive constant equilibrium, but has no influence on the stability of the trivial equilibrium and the semi-trivial equilibrium. We then derive Hopf bifurcation and steady state bifurcation related to prey-taxis, which imply that the prey-taxis plays an important role in the dynamics. [ABSTRACT FROM AUTHOR]

In this paper, we have considered a Lorenz-like model with slight changes in the nonlinear terms. Here we have studied the system dynamics for different range of values of parameters σ , r . The Hopf bifurcation analysis of the system has been done using center manifold theorem for σ = - 1 , r > 1 . Phase portraits of solutions of the system are plotted for various system parameters to substantiate the change in dynamics. The bifurcation diagram and the Lyapunov exponent evaluation plots also help to explain the behaviour of the system. Using Fishing principle, we have shown the existence of homoclinic orbit and consequently, observed the existence of homoclinic as well as heteroclinic orbits in the numerical simulation for σ > 0 , r > 1 . [ABSTRACT FROM AUTHOR]

The greatest cause of death worldwide continues to be cancer, a complicated set of diseases characterized by uncontrolled cell development. Although early identification and therapeutic approaches have improved, the incidence of the disease is still on the rise, demanding continued study into its underlying causes and cutting-edge treatment paradigms. For creative interventions and focused medicines, the variety of cancer kinds, which are influenced by genetics, way of life, and environmental variables, poses both difficulties and opportunities. In this paper, we present a mathematical model to treat cancer with combined therapies, oncolytic viruses and Mitogen-activated protein kinase inhibitors. We demonstrate that our model is both biologically and mathematically well-posed through the existence, the non-negativity and the boundedness of solutions. Furthermore, we study the equilibrium points as well as the stability of these equilibria. Finally, we use numerical simulations to illustrate the effect of this combined therapy on tumor cells. [ABSTRACT FROM AUTHOR]

This paper focuses on the Hopf bifurcation of a fractional tri-neuron network with both leakage delay and communication delay under different fractional orders. By applying fractional Laplace transform, the stability theorem of linear autonomous system and Hopf bifurcation theorem, we obtain a class of asymptotic stability criterion of zero solution as well as delay-induced Hopf bifurcation conditions for the considered system. Simultaneously, the stability and Hopf bifurcation for tri-neuron network with single fractional order are also discussed as a special case of our proposed neural network model. Finally, a simulation example is given to illustrate the efficiency of the presented theoretical results in this paper. [ABSTRACT FROM AUTHOR]

This paper is concerned with a delayed reaction–diffusion equation on a unit disk. By means of the singularity theory and Lyapunov–Schmidt reduction, we not only derive universal conclusions about the existence of inhomogeneous steady-state solutions and the equivariant Hopf bifurcation theorems, but also obtain some more extraordinary properties of bifurcating solutions, which are produced by the radial symmetry through abstract methods based on the Lie group representation theory. Meanwhile, we illustrate our results by an application to a population model with a time delay. Furthermore, the methods established in this paper are applicable to specific delayed reaction–diffusion models with other symmetries. [ABSTRACT FROM AUTHOR]

In this paper, we consider a delayed single population model with patch structure, and investigate Hopf bifurcations when the dispersal rate or the scaling parameter of the growth rate is small. The effect of dispersal patterns is analyzed. We show that dispersal patterns affect the occurrence of Hopf bifurcations when the scaling parameter of the growth rate is small, and affect the values of Hopf bifurcations when the dispersal rate is small. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the spatiotemporal dynamics of the Sel'kov–Schnakenberg system. The stability of the positive constant steady state is studied by the linear stability theory. Hopf bifurcation and Turing–Hopf bifurcation are generated by varying two parameters in the model. The normal form near the Turing–Hopf singularity is calculated to explore the complex dynamics of the system. Finally, numerical simulations are carried out to verify the theoretical results. Our results show that the Sel'kov–Schnakenberg system exhibits complex dynamics near the Turing–Hopf singularity, including the existence of inhomogeneous steady states, homogeneous periodic solutions and inhomogeneous periodic solutions. [ABSTRACT FROM AUTHOR]

In this paper, a Leslie–Gower model with weak Allee effect on prey and fear effect on predator is proposed. Compared with the case without fear effect on predator, the new model undergoes richer dynamic behaviors such as saddle-node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation. Also, different from the strong Allee effect on prey, the system with weak Allee effect has bistable attractors which are a largely stable limit cycle and a stable positive equilibrium, two stable equilibria, or a stable limit cycle and a stable trivial equilibrium. When the Allee effect coefficient is intermediate, fear effect on the predator can protect the prey and the predator from being extinguished. The results in this paper can be seen as a complement to those in the literatures about the Leslie–Gower model with Allee effect and fear effect. [ABSTRACT FROM AUTHOR]

This paper studies an Internet congestion control system with two time delays, which are accessed by a single resource and considers both discrete and distributed delays of the system. By designing a new hybrid controller containing negative feedback control and time delay feedback control to control the system, and taking discrete time delay variables as bifurcation parameters, the local stability and Hopf bifurcation of the system are studied. The results show that the Hopf bifurcation can be effectively delayed or avoided by adjusting the value of the feedback control parameter β . The global asymptotically stable dynamic characteristics of the system are ideal, which has important functional significance for optimizing network congestion control. Finally, a large number of simulation examples verify the correctness of the conclusions. [ABSTRACT FROM AUTHOR]

In this essay, we introduce a bioeconomic predator–prey model which incorporates the square root functional response and nonlinear prey harvesting. Due to the introduction of nonlinear prey harvesting, the model demonstrates intricate dynamic behaviors in the predator–prey plane. Economic profit serves as a bifurcation parameter for the system. The stability and Hopf bifurcation of the model are discussed through normal forms and bifurcation theory. These results reveal richer dynamic features of the bioeconomic predator–prey model which incorporates the square root functional response and nonlinear prey harvesting, and provides guidance for realistic harvesting. A feedback controller is introduced in this paper to move the system from instability to stability. Moreover, we discuss the biological implications and interpretations of the findings. Finally, the results are validated by numerical simulations. [ABSTRACT FROM AUTHOR]

Analysing the prey-predator model is the purpose of this paper. In interactions of the Beddington–DeAngelis type, the predator consumes its prey. Researchers first examine the existence and local stability of potential unbalanced equilibrium boundaries for the model. In addition, for the suggested model incorporating the prey refuge, we investigate the Hopf bifurcation inquiry. To emphasise our key analytical conclusions, we show some numerical simulation results at the end. [ABSTRACT FROM AUTHOR]

The study of harvesting mechanisms in predator-prey systems with an Allee effect on prey has always garnered significant attention. In this paper, the dynamics and harvesting strategies of a predator-prey system are investigated, where the prey is subject to the Allee effect. The positivity and boundedness of solutions, the existence and stability of equilibria are further studied. The existence of a Hopf bifurcation at the interior equilibrium point of the system is investigated and verified by numerical simulations. Furthermore, we investigate the maximum sustainable yield (MSY), maximum sustainable total yield (MSTY) and the optimal economic profit of the proposed system. We find that MSY can be attained through predator harvesting, while MSTY is observed when harvesting efforts are uniform across species. In these situations, the biological system maintains stability. Using the method of control parametrization, the optimal economic profit and harvesting strategy are obtained. The results show that the harvesting efforts can affect the stability of the system, resulting in several interesting biological phenomena. This research provides a theoretical basis for biological resource management. [ABSTRACT FROM AUTHOR]

The dynamics of prey–predator system, when one or both the species are harvested non-linearly, has become a topic of intense study because of its wide applications in biological control and species conservation. In this paper we have discuss different bifurcation analysis of a two dimensional prey–predator model with Beddington–DeAngelis type functional response in the presence of prey refuge and non-linear harvesting of both species. We have studied the positivity and boundedness of the model system. All the biologically feasible equilibrium points are investigated and their local stability is analyzed in terms of model parameters. The global stability of coexistence equilibrium point has been discussed. Depending on the prey harvesting effort ( E 1 ) and degree of competition among the boats, fishermen and other technology ( l 1 ) used for prey harvesting, the number of axial and interior equilibrium points may change. The system experiences different type of co-dimension one bifurcations such as transcritical, Hopf, saddle-node bifurcation and co-dimension two Bogdanov–Takens bifurcation. The parameter values at the Bogdanov–Takens bifurcation point are highly sensitive in the sense that the nature of coexistence equilibrium point changes dramatically in the neighbourhood of this point. The feasible region of the bifurcation diagram in the l 1 - E 1 parametric plane divides into nine distinct sub-regions depending on the number and nature of equilibrium points. We carried out some numerical simulations using the Maple and MATLAB software to justify our theoretical findings and finally some conclusions are given. [ABSTRACT FROM AUTHOR]

In this paper, a fractional model of a special structure of bidirectional associative memory (BAM) neural networks called tri-diagonal BAM neural networks (TdBAMNNs) is considered. The Hopf bifurcation analysis is made for the proposed fractional system in the presence of leakage and communication delays. The feasibility of the obtained theoretical results is verified by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper is concerned with the general Langford system under homogeneous Neumann boundary conditions. The stabilities of constant solutions are discussed for the general Langford ODE and PDE systems, respectively. Based on the stability results, for the Langford ODE system, the existence, bifurcation direction and stability of periodic solutions are established. Then for the Langford PDE system, by the center manifold theory and the normal form method, the direction of Hopf bifurcation and the stability of spatially homogeneous periodic solutions are investigated. Finally, numerical simulations are shown to support and supplement the results of theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we propose a predator–prey model with prey refuge and fear effect under non-diffusion and diffusion. For the non-diffusion ODE model, we first analyze the existence and stability of equilibria. Then, the existence of transcritical bifurcation, Hopf bifurcation and limit cycle is discussed, respectively. We find that when the cost of minimum fear η is taken as the bifurcation parameter, it not only influence the occurrence of Hopf bifurcation but also alters its direction. For diffusion predator–prey model under homogeneous Neumann boundary conditions, we observe that the Turing instability does not occur, but the Hopf bifurcation will manifest near the interior equilibrium. By considering η as the bifurcation parameter, the direction and stability of spatially homogeneous periodic orbits are established. At last, the validity of the theoretical analysis are verified by a series of numerical simulations. The results indicate that prey refuge and fear effect play an key role in the stability of populations. [ABSTRACT FROM AUTHOR]

This paper focuses on a cholera model with temporary immunity and recovery-age. We first investigate the existence of unique solution to the model by reformulating the system as an abstract Cauchy problem, and present the basic reproduction number. By analyzing the characteristic equation, we discuss the stability of the steady states and further verify the existence of Hopf bifurcation. The theoretical results show that the temporary immunity effect takes a crucial effect on the perturbation around the endemic equilibrium. Numerical simulations are performed to support our results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the Crowley–Martin functional response and nonlocal competition into a reaction–diffusion immunosuppressive infection model. First, we analyze the existence and stability of the positive constant steady states of the systems with nonlocal competition and local competition, respectively. Second, we deduce the conditions for the occurrence of Turing, Hopf, and Turing–Hopf bifurcations of the system with nonlocal competition, as well as the conditions for the occurrence of Hopf bifurcations of the system with local competition. Furthermore, we employ the multiple time scales method to derive the normal forms of the Hopf bifurcations reduced on the center manifold for both systems. Finally, we conduct numerical simulations for both systems under the same parameter settings, compare the impact of nonlocal competition, and find that the nonlocal term can induce spatially inhomogeneous stable periodic solutions. We also provide corresponding biological explanations for the simulation results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a reaction-diffusion model incorporating dynamic variables for nutrient, phytoplankton, and zooplankton. Moreover, we account for the impact of time delay in the growth of phytoplankton following nutrient uptake. Our theoretical analysis reveals that the time delay can trigger the emergence of persistent oscillations in the model via a Hopf bifurcation. We also analytically track the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions. Our simulation results demonstrate stability switches occurring for the positive equilibrium with an increasing time lag. Furthermore, the model exhibits homogeneous periodic-2 and 3 solutions, as well as chaotic behaviour. These findings highlight that the presence of time delay in the phytoplankton growth can bring forth dynamical complexity to the nutrient-plankton system of aquatic habitats. [ABSTRACT FROM AUTHOR]

This paper is devoted to the high codimension bifurcations of a classical predator–prey system with Allee effects and generalized Holling type III functional response p (x) = m x 2 a x 2 + b x + 1 where b > - 2 a . We show that the maximal orders of nilpotent saddle, cusp singularity and weak focus are all three. The unfoldings of a cusp singularity and of a nilpotent saddle of order 3 with a fixed invariant line are developed. The dependence of codimension of degenerate Hopf bifurcation on b is thoroughly investigated. It is proven that there exist a homoclinic loop of order 2 and a heteroclinic loop of order 2 for - 2 a < b < 0 , and three limit cycles for b > 0 . Together with existing work for Holling type I, II and IV functional responses, our results complement the analysis of the classical predator–prey systems with Allee effects and four types of Holling functional responses. Furthermore, simple formulas are derived to characterize the order of nilpotent saddle, through which the existence and order of the heteroclinic loop can be easily obtained for a general class of predator–prey systems with any smooth functional response. [ABSTRACT FROM AUTHOR]

This paper is devoted to the existence, multiplicity, stability, and Hopf bifurcation of steady-state solutions of a diffusive Lotka–Volterra type model for two species with nonlocal delay effect and nonlinear boundary condition. It is found that there is no Hopf bifurcation when the interior reaction term is weaker than the boundary reaction term, and that the interior reaction delay determines the existence of Hopf bifurcation only when the interior reaction term is stronger than the boundary reaction term. This observation helps us to understand the nonlinear balance between the interior reaction and boundary flux in nonlinear boundary problems. Moreover, the general results are illustrated by applications to a model with homogeneous kernels. [ABSTRACT FROM AUTHOR]

The tea green leafhopper Empoasca onukii is one kind of insect pest threatening the tea production, and the mite Anystis baccarum has been used as an agent for pest control. In this paper, we introduce a generalist predator-prey model to study the dynamics for informing biological control. There have been some bifurcation studies of the generalist predator-prey model in the last few years. Except for the bifurcations include saddle-node bifurcation of codimension 1 and 2, Hopf bifurcations, and Bogdanov-Takens bifurcation of codimension 2 and 3, we also present the bifurcations of nilpotent singularities of elliptic and focus type of codimension 3. We find that the nilpotent singularities are associated with a cubic Liénard system, and the nilpotent bifurcations are three-parameter bifurcations of a codimension 4 nilpotent focus. Furthermore, we show that the nilpotent focus serves as an organizing center to connect all the codimension 3 bifurcations in the system. We also present the bifurcation diagrams to unfold the nilpotent singularities of codimension 3. One interesting observation is that we show numerically the existence of three limit cycles in the system. [ABSTRACT FROM AUTHOR]

In this paper, we consider a single species population model over patches with delay and nonlocal interactions, for which no symmetry for the dispersion (connection) matrix is assumed. We show that there exists a positive equilibrium when the dispersal rate is large. We also discuss the stability/instability of this positive equilibrium, establish the threshold dynamics and explore the associated Hopf bifurcation. Moreover, we demonstrate our theoretical results by a nonlocal logistic population model and by the Nicholson's blowflies model. [ABSTRACT FROM AUTHOR]

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]

This paper makes a new breakthrough in deliberating the bifurcations of fractional-order bidirectional associative memory neural network (FOBAMNN). In the beginning, the corresponding bifurcation results are established according to self-regulating parameter, which is different from bifurcation outcomes available by using time delay as the bifurcation parameter, and greatly enriches the bifurcation results of continuous neural networks(NNs). The deived results manifest that a larger self-regulating parameter is more conducive to the stability of the system, which is consistent with the actual meaning of the self-regulating parameter representing the decay rate of activity. In addition to the innovation in the research object, this paper also has innovation in the procedure of calculating the bifurcation critical point. In the face of the quartic equation about the bifurcation parameters, this paper utilizes the methodology of implicit array to calculate the bifurcation critical point succinctly and effectively, which eschews the disadvantages of the conventional Ferrari approach, such as cumbersome formula and huge computational efforts. Our developed technique can be employed as a general method to solve the bifurcation point including the problem of dealing with the bifurcation critical point of delay. Ultimately, numerical experiments test the key theoretical fruits of this paper. [ABSTRACT FROM AUTHOR]

The bidirectional associative memory (BAM) neural network has the capability to store hetero-associative pattern pairs, which has high requirements for stability. This paper inquires into Hopf bifurcation of fractional-order bidirectional associative memory neural network (FOBAMNN) and implants three types of delays into the FOBAMNN. Namely leakage delay, self-connection delay, and communication delay, both of which are unequal. Drawing support from matrix eigenvalue theory, stability theory of fractional differential equations and bifurcation technology, The delay-dependent stability criterion and bifurcation point of the model are established by exploiting the characteristic polynomial. Afterwards, the self-connection delay or leakage delay is selected as the bifurcation parameter, and the unselected delay of the two is fixed in its stable interval, so as to obtain the condition of bifurcation. The results show that different types of delay affect the stability of the system. Simultaneously, once the delay outreaches the critical value of bifurcation, the stability of the model will be wrecked. Thereupon, in the application, we should adopt small delays to maintain the stability of the system. We illustrate that the leakage delay and self-connection delay can affect the stability of FOBAMNN. And the calculation method of the critical value of the delay will also be given. At length, the authenticity of the developed key fruits is elucidated via numerical simulations. [ABSTRACT FROM AUTHOR]

Under the background of double carbon, it is important to study forest pests and diseases to improve forest carbon sink. In this paper, we establish a delayed model associated with the larvae and adults of Saperda populnea, susceptible poplars, and infected poplars. First, we analyze the existence and stability of the equilibrium of the model. Second, we study the existence of Hopf bifurcation near the equilibrium and obtain the normal form of Hopf bifurcation by the multiple time scales method. Then, we analyze the direction and stability of Hopf bifurcating periodic solutions. Third, we analyze and conjecture some parameter values based on official data, and carry out numerical simulations to verify our results. Finally, we give some suggestions on the prevention and control of Saperda populnea. [ABSTRACT FROM AUTHOR]

This paper introduces diffusion into an immunosuppressive infection model with virus stimulation delay and Beddington-DeAngelis functional response. First, we study the stability of positive constant steady state solution and show that the Hopf bifurcation will exist under certain conditions. Second, we derive the normal form of the Hopf bifurcation for the model reduced on the center manifold by using the multiple time scales (MTS) method. Moreover, the direction and stability of the bifurcating periodic solution are investigated. Finally, we present numerical simulations to verify the results of theoretical analysis and provide corresponding biological explanations. [ABSTRACT FROM AUTHOR]

In this paper, a six-neuron incommensurate fractional order BAM neural network model with multi-delays is considered. We demonstrate that the equilibrium point of the system loses its stability and Hopf bifurcation emerges when the delay passes through a critical value. And the relationship between the critical delay of Hopf bifurcation and size of fractional orders is found. Finally, some numerical simulations are given to verify the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper proposes a diffusive predator–prey model with Allee effect, time delay and anti-predator behavior. First, the existence and stability of all equilibria are analyzed and the conditions for the appearance of the Hopf bifurcation are studied. Using the normal form and center manifold theory, the formulas which can determine the direction, period and stability of Hopf bifurcation are obtained. Numerical simulations show that the Allee effect can determine the survival abundance of the prey and predator populations, and anti-predator behavior can greatly improve the stability of the coexisting equilibrium. [ABSTRACT FROM AUTHOR]

Purpose: In order to reduce the hazards caused by the nonlinear torsional vibration of the shaft system of the direct-drive permanent magnet wind turbine, the dynamic characteristics of the controlled shaft system torsional vibration were analyzed. Methods: First, the shaft system of the direct-drive permanent magnet wind turbine is equivalent to a two-mass model. Based on considering the electromechanical coupling and the nonlinear change of the main shaft damping, the torsional vibration dynamic model of the shaft system is established by the Lagrange–Maxwell equation. Second, with the main shaft damping as the bifurcation parameter, the Routh–Hurwitz criterion is used to calculate the Hopf bifurcation critical point and stability range of the shafting system. Finally, a nonlinear state feedback controller is designed, and the controlled shafting system paradigm is obtained by the direct method. Results: The torsional vibration characteristics of shafting and the influence of supercritical Hopf bifurcation on shafting are discussed. In order to suppress the unstable torsional vibration of the shafting system and analyze the influence of the controller's linear gain and nonlinear gain on the torsional vibration of the shafting system, the numerical simulation verifies the correctness of the theoretical analysis. Conclusions: This paper can provide a theoretical basis for the stable operation of the direct-drive permanent magnet wind turbine. [ABSTRACT FROM AUTHOR]

Chameleon chaotic systems are nonlinear dynamical systems whose chaotic attractors can transform between hidden and self-excited types by tuning system parameters to modify equilibrium points. This paper proposes a novel family of chameleon chaotic systems, which can exhibit three types of chaotic attractors: self-excited attractors with a nonhyperbolic equilibrium, hidden attractors with a stable equilibrium, and hidden attractors with no equilibrium points. Bifurcation analysis uncovers the mechanisms by which self-excited and hidden chaotic attractors arise in this family of chameleon systems. It is demonstrated that various forms of chaos emerge through period-doubling routes associated with changes in the coefficient of a linear term. An electronic circuit is designed and simulated in Multisim to realize a hidden chaotic system with no equilibrium points. It is demonstrated that the electronic circuit simulation is consistent with the theoretical model. This research has the potential to enhance our comprehension of chaotic attractors, especially the hidden chaotic attractors. [ABSTRACT FROM AUTHOR]