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Xu R.,Shijiazhuang Mechanical Engineering College
Nonlinear Analysis: Real World Applications | Year: 2011

A stage-structured predatorprey system with Holling type-II functional response and time delay due to the gestation of predator is investigated. By analyzing the characteristic equations, the local stability of each of feasible equilibria of the system is discussed and the existence of a Hopf bifurcation at the coexistence equilibrium is established. By means of the persistence theory on infinite dimensional systems, it is proven that the system is permanent if the coexistence equilibrium exists. By using Lyapunov functionals and LaSalle invariant principle, it is shown that the trivial equilibrium is globally stable when both the predator-extinction equilibrium and the coexistence equilibrium are not feasible, and that the predator-extinction equilibrium is globally asymptotically stable if the coexistence equilibrium does not exist, and sufficient conditions are derived for the global stability of the coexistence equilibrium. Numerical simulations are carried out to illustrate the main theoretical results. © 2011 Elsevier Ltd. All rights reserved.


The issue of exponential synchronization for Cohen-Grossberg neural networks with mixed time-varying delays, stochastic noise disturbance and reaction-diffusion effects is investigated. An approach combining Lyapunov stability theory with stochastic analysis approaches and periodically intermittent control is taken to investigate this problem. The proposed criterion for exponential synchronization generalizes and improves those reported recently in the literature. This paper also presents an illustrative example and uses simulated results of this example to show the feasibility and effectiveness of the proposed scheme. © 2012 Elsevier Ltd.


This paper investigates the synchronization problem of generalized stochastic neural networks with mixed time-varying delays and reaction-diffusion terms using linear feedback control. Lyapunov stability theory combining with stochastic analysis approaches is employed to derive sufficient criteria ensuring the coupled chaotic generalized stochastic neural networks to be globally exponentially synchronized. The generalized neural networks model considered includes reaction-diffusion Hopfield neural networks, reaction-diffusion bidirectional associative memory neural networks, and reaction-diffusion cellular neural networks as its special cases. It is theoretically proven that these synchronization criteria are more effective than some existing ones. This paper also presents some illustrative examples and uses simulated results of these examples to show the feasibility and effectiveness of the proposed scheme. © 2012 Elsevier B.V.


Xu R.,Shijiazhuang Mechanical Engineering College
Nonlinear Dynamics | Year: 2012

A Holling type predator-prey model with stage structure for the predator and a time delay due to the gestation of the mature predator is investigated. By analyzing the characteristic equations, the local stability of a predator-extinction equilibrium and a coexistence equilibrium of the model is addressed and the existence of Hopf bifurcations at the coexistence equilibrium is established. By means of the persistence theory on infinite dimensional systems, it is proven that the system is permanent if the coexistence equilibrium is feasible. By using Lyapunov functionals and the LaSalle invariance principle, it is shown that the predator-extinction equilibrium is globally asymptotically stable when the coexistence equilibrium is not feasible, and sufficient conditions are derived for the global stability of the coexistence equilibrium. Numerical simulations are carried out to illustrate the main theoretical results. © 2011 Springer Science+Business Media B.V.


Gan Q.,Shijiazhuang Mechanical Engineering College
Nonlinear Dynamics | Year: 2012

In this paper, the problem of exponential synchronization is investigated for a class of stochastic perturbed chaotic neural networks with both mixed time delays and reaction-diffusion terms. By employing Lyapunov-Krasovskii functional and stochastic analysis approaches, an adaptive controller is designed to guarantee the exponential synchronization of proposed neural networks in the mean square. In particular, the mixed time delays in this paper synchronously consist of constant delay in the leakage term (i.e., "leakage delay"), discrete time-varying delay and distributed time-varying delay which are more general than those discussed in the previous literature. Furthermore, our synchronization criteria are easily verified and do not need to solve any linear matrix inequality. Therefore, the results obtained in this paper generalize and improve those given in the previous literature. Finally, the extensive simulations are performed to show the effectiveness and feasibility of the obtained method. © Springer Science+Business Media B.V. 2012.

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