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1.
In this paper, a hybrid triple delayed prey predator bioeconomic system with prey refuge and Lévy jumps is established, where both maturation delay for prey and predator population and gestation delay for predator population are considered. For deterministic system, positivity and uniform permanence of solution are discussed. Local stability of deterministic system around interior equilibrium is investigated due to variations of triple time delays. For stochastic system without time delay, sufficient conditions for stochastically ultimate boundedness and stochastic permanence are discussed. Existence of stochastic Hopf bifurcation and stochastic stability are investigated. For stochastic system with triple time delays, existence and uniqueness of global positive solution are studied. Finally, combined dynamic effects of triple time delays and Lévy jumps on the hybrid stochastic system are discussed by constructing appropriate Lyapunov functions. Numerical simulations are supported to illustrate theoretical analysis.  相似文献   

2.
A differential-algebraic model system which considers a prey-predator system with stage structure for prey and harvest effort on predator is proposed. By using the differential-algebraic system theory and bifurcation theory, the dynamic behaviors of the proposed model system with and without discrete time delay are investigated. Local stability analysis of the model system without discrete time delay reveals that there is a phenomenon of singularity induced bifurcation due to variation of the economic interest of harvesting, and a state feedback controller is designed to stabilize the proposed model system at the interior equilibrium; on the other hand, the local stability of the model system with discrete time delay is also studied. The theoretical analysis shows that the discrete time delay has a destabilizing effect in the model of population dynamics, and a phenomenon of Hopf bifurcation occurs as the discrete time delay increases through a certain threshold. Numerical simulations are carried out to show the consistency with theoretical analysis.  相似文献   

3.
In this paper, a discrete-time seasonally forced SIR epidemic model is investigated for different types of bifurcations. Although, many researchers already suggested numerically that this model can exhibit chaotic dynamics but not much focus is given to the bifurcation theory of the model. We prove analytically and numerically the existence of different types of bifurcations in the model. First, the one and two parameters bifurcations of this model are investigated by computing their critical normal form coefficients. Secondly, the flip, Neimark–Sacker, and strong resonances bifurcations are detected for this model. The critical coefficients identify the scenario associated with each bifurcation. The complete complex dynamical behavior of the model is investigated. Some graphical representations of the model are presented to verify the obtained results.  相似文献   

4.
A three-degree-of-freedom vibro-impact system is considered. The nonlinear dynamical model and the six-dimensional Poincaré map are established and the dynamical behaviors of the system, including double Neimark–Sacker bifurcation, torus T2 and its routes to chaos, is investigated by numerical simulations. As the control parameters vary, the torus T2 changes into multi-circle torus T1 via one-frequency phase locking on its position, which are divided into longitude circles and latitude circles, and the system keeps quasi-periodic motion. Further the impact motion settles into periodic orbit via two-frequency phase locking, then the system leads eventually to chaos. The second route to chaos shows, by establishing the secondary Poincaré section, that the torus T2 leads to chaos via torus doubling bifurcation and there may exist torus doubling cascade.  相似文献   

5.
In this paper, we consider the problem of Hopf bifurcation control for a complex network model with time delays. We know that for the system without control, as the positive gain parameter of the system passes a critical point, Hopf bifurcation occurs. To control the Hopf bifurcation, a time-delayed feedback controller is proposed to delay the onset of an inherent bifurcation when such bifurcation is undesired. Furthermore, we can also change the stability and direction of bifurcating periodic solutions by choosing appropriate control parameters. Numerical simulation results confirm that the new feedback controller using time delay is efficient in controlling Hopf bifurcation.  相似文献   

6.
In this paper, a delayed feedback controller with the delay-dependent coefficient is introduced into a multiple delay phytoplankton-zooplankton system. For uncontrolled system, choosing delays as the bifurcation parameters, we prove that Hopf bifurcation can occur when the delays change and cross some values. Then, the delays are still chosen as the bifurcation parameters to research the dynamic behaviors of the controlled system. Under this control mechanism, the onset of Hopf bifurcation can be delayed by selecting the appropriate control parameters and the stability domain can be extended as feedback gain (the decay rate) decreases (increases), and the influence of the decay rate cannot be ignored. Furthermore, using the crossing curve methods, the stable changes of equilibrium in two delay plane can be obtained. Some numerical simulations are given to verify the correctness and validity of the delayed feedback controller in the bifurcation control.  相似文献   

7.
The problem of bifurcation for delayed fractional neural networks(FNNs) with single delay has been considerably researched. It is more realistic to portray the dynamical properties of FNNs with multiple delays, but this has been not investigated before. This paper attempts to conduct a research on the stability and bifurcation for a FNN with double delays. The criteria of heterogeneous delays-induced bifurcations are decidedly procured. Then, the influence of solitary delay on the bifurcation point is ulteriorly displayed by delicate computation. It is demonstrated that the stability performance of the proposed FNN can be undermined or enhanced by varying properly time delay. Finally, illustrative examples are addressed to validate the availability of the proposed results.  相似文献   

8.
By transforming an exact stability condition, a new Nyquist-like plot is proposed to predict occurrences of three typical instabilities in DC–DC converters. The three instabilities are saddle-node bifurcation (coexistence of multiple solutions), period-doubling bifurcation (subharmonic oscillation), and Neimark bifurcation (quasi-periodic oscillation). In a single plot, it accurately predicts whether an instability occurs and what type the instability is. The plot is equivalent to the Nyquist plot, and it is a useful design tool to avoid these instabilities. Four examples are used to illustrate the accuracy of this new plot to predict instabilities in the buck or boost converter with fixed or variable switching frequency.  相似文献   

9.
This paper deals with the problem of stabilization for a class of hybrid systems with time-varying delays. The system to be considered is with nonlinear perturbation and the delay is time varying in both the state and control. Using an improved Lyapunov–Krasovskii functional combined with Newton–Leibniz formula, a memoryless switched controller design for exponential stabilization of switched systems is proposed. The conditions for the exponential stabilization are presented in terms of the solution of matrix Riccati equations, which allow for an arbitrary prescribed stability degree.  相似文献   

10.
In this paper, a delayed fractional eco-epidemiological model with incommensurate orders is proposed, and a control strategy of this model is discussed. Firstly, for the system with no controller, the stability and Hopf bifurcation with respect to time delay are investigated. Secondly, under the influence of the controller, the stability and Hopf bifurcation of the system is discussed, and it is indicated that the stability of the system can be changed by increasing the feedback control delay. In particular, a separate study is carried out on the bifurcation with respect to the extended feedback delay, and the bifurcation point is calculated. At last, to support the theoretical results, some numerical simulations are depicted.  相似文献   

11.
This paper investigates the problem for stability of neutral-type dynamical neural networks involving delay parameters. Different form the previously reported results, the states of the neurons involve multiple delays and time derivative of states of neurons include discrete time delays. The stability of such neural systems has not been given much attention in the past literature due to the difficulty of finding Lyapunov functionals which are suitable for stability analysis of this type of neural networks. This paper constructs a generalized Lyapunov functional by introducing new terms into the well-known Lyapunov functional that enables us to conduct a theoretical investigation into stability analysis of delayed neutral-type neural systems. Based on this modified novel Lyapunov functional, sufficient criteria are derived, which guarantee the existence, uniqueness and global asymptotic stability of the equilibrium point of the neutral-type neural networks with multiple delays in the states and discrete delays in the time derivative of the states. The applicability of the proposed stability conditions rely on testing two basic matrix properties. The constraints impose on the system matrices are determined by using nonsingular M-matrix condition, and the constraints imposed on the coefficients of the time derivative of the delayed state variables are derived by exploiting the vector-matrix norms. We also note that the obtained stability conditions have no involvement with the delay parameters and expressed in terms of nonlinear Lipschitz activation functions. We present a constructive numerical example for this class of neural networks to give a systematic procedure for determining the imposed conditions on the whole system parameters of the delayed neutral-type neural systems.  相似文献   

12.
In this paper, the robust exponential stability of uncertain impulsive delay difference equations is investigated. First, some robust exponential stability criteria for uncertain impulsive delay difference equations with continuous time in which the state variables on the impulses may relate to the time-varying delays are provided. Then a robust exponential stability result for uncertain linear impulsive delay difference equations with discrete time is given. Some examples, including an example which cannot be studied by the existing results, are also presented to illustrate the effectiveness of the obtained results.  相似文献   

13.
In this paper, an eco-epidemiological predator–prey model with time delay representing the gestation period of the predator is investigated. In the model, it is assumed that the predator population suffers a transmissible disease by contact. By analyzing corresponding characteristic equations, the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the disease-free equilibrium, the prey–infected predator equilibrium and the endemic-coexistence equilibrium are established. By means of Lyapunov functionals and LaSalle's invariance principle, sufficient conditions are obtained for the global asymptotic stability of the predator-extinction equilibrium, the disease-free equilibrium, the prey–infected predator equilibrium and the endemic-coexistence equilibrium of the model.  相似文献   

14.
This paper considers existence, uniqueness and the global asymptotic stability of fuzzy cellular neural networks with mixed delays. The mixed delays include constant delay in the leakage term (i.e., “leakage delay”), time-varying delays and continuously distributed delays. Based on the Lyapunov method and the linear matrix inequality (LMI) approach, some sufficient conditions ensuring global asymptotic stability of the equilibrium point are derived, which are dependent on both the discrete and distributed time delays. These conditions are expressed in terms of LMI and can be easily checked by MATLAB LMI toolbox. In addition, two numerical examples are given to illustrate the feasibility of the result.  相似文献   

15.
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16.
Sampled-data control for time-delay systems   总被引：1，自引：0，他引：1  
The sampled-data systems are hybrid ones involving continuous time and discrete time signals, which makes the traditional analysis and synthesis methodologies of time-delay systems unable to be directly used in the cases of hybrid systems with time-delay. The primary disadvantages of current design techniques of sampled-data control are their inabilities to deal effectively with time-delay and the model uncertainty. In this paper, we generalized the analysis methodology of time-delay systems to that of the hybrid systems with time-delay and uncertainty, which developed a design procedure of sampled-data control for time-delay systems. Asymptotic stability of the time-delay hybrid systems was developed. The time-delay dependent robust sampled-data control for the time-varying delay of an uncertain linear system was then discussed. The results were described as linear matrix inequalities, which can be solved using newly released LMITool.  相似文献   

17.
In this paper, we investigate an eco-epidemic model with distributed time delay and impulsive control strategy. Firstly, by using Floquet theory of impulsive differential equation, we get the condition for the local stability of the prey eradication periodic solutions. Secondly, by means of impulsive equation compare theory, we get the condition for the global asymptotical stability of the prey eradication periodic solutions. Finally we study the permanence of the system. Numerical simulations (bifurcation diagram, the largest Lyapunov exponents and power spectra) are carried out to illustrate the above theoretical analysis and the rich dynamics phenomenon, which are caused by impulsive effects and time delay, for example bifurcation, double period solution, etc.  相似文献   

18.
By using the Razumikhin-type technique, for stochastic discrete-time delay systems, this paper establishes the discrete Razumikhin-type theorems on the pth moment stability, the global pth moment stability and the pth moment exponential stability, respectively. The almost sure exponential stability is also investigated by using the pth moment exponential stability and the Borel–Cantelli lemma. As the applications of t he established theorems, stability of a special class of stochastic discrete-time delay systems, synchronization of the stochastic discrete-time delay dynamical networks and stabilization of a stochastic discrete-time linear delay time invariant system are examined.  相似文献   

19.
In this paper, we propose a diffusive prey-predator system with mutually interfering predator (Crowley–Martin functional response) and prey reserve. In particular, we develop and analyze both spatially homogeneous model based on ordinary differential equations and reaction-diffusion model. We mainly investigate the global existence and boundedness of positive solution, stability properties of homogeneous steady state, non-existence of non-constant positive steady state, conditions for Turing instability and Hopf bifurcation of the diffusive system analytically. Conventional stability properties of the non-spatial counterpart of the system are also studied. The analysis ensures that the prey reserve leaves stabilizing effect on the stability of temporal system. The prey reserve and diffusive parameters leave parallel impact on the stability of the spatio-temporal system. Furthermore, we illustrate the spatial patterns via numerical simulations, which show that the model dynamics exhibits diffusion controlled pattern formation by different interesting patterns.  相似文献   

20.
Bifurcation theory is commonly used to study the dynamical behavior of ecosystems. It involves the analysis of points in the parameter space where the stability of the system changes qualitatively. The type of bifurcation that associates equilibria with periodic solution is called Hopf bifurcation. In this paper, a life energy system dynamic model of two components with multiple delays is presented. It is shown that the interaction parameters of the delayed ecosystem play a fundamental role in classifying the rich dynamics and bifurcation phenomena. Regarding the combined interaction parameter as a bifurcation parameter, the bifurcation values in the parameter plane are displayed. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by applying the normal form theory and the center manifold theorem. Moreover, the amplitudes of oscillations always increase as the interaction parameters increase, while the robustness of periods occurs as the interaction parameters vary. From an ecological point of view, the existence of Hopf bifurcation expresses periodic oscillatory behavior of the life energy system.  相似文献   

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