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Scalar feedback control in a chaotic discrete prey predator system is investigated. The existence of the fixed points and the local stability of the positive fixed point are discussed. By using center manifold theorem, it is proved rigorously that the system undergoes the flip bifurcation near the unique positive fixed point. To eliminate the undesirable chaos induced by the flip bifurcation and stabilize...
This paper is devoted to study the problem of a partially dependent predator-prey model with time delay. The effect of delay on the stability of the interior positive equilibrium is investigated, and the conditions for existence of Hopf bifurcations are given. Finally, numerical simulations are carried out to illustrate our analytical results, the largest Lyapunov exponent is computed, and the chaotic...
A three species food chain model with time delayed harvesting is concerned. By using the theory of functional differential equation and Hassard's method, the conditions on which positive equilibrium exists and Hopf bifurcation occurs are given. Finally numerical simulations are performed to support the analytical results, and the chaotic behaviors are observed.
One dynamic model has been established in ecological system. Considering the influence of foreign trade on the ecological footprint and ecological carrying capacity, the stability analysis of the system has been given. The influence of the parameter on the system has been discussed while the other conditions were fixed. Then the Variable feedback chaos control method is successfully applied to stabilize...
By using the method of dynamical systems, this paper researches the exact travelling wave solutions and bifurcation for the modified ZK equation. As a result, exact implicit parametric representations of some solitary wave solutions and periodic wave solutions, as well as some exact solutions are given.
In present paper, the time-delayed feedback is coupled with a ratio-dependent predator-prey model of Holling □ type. This predator-prey system can be seen as a human-controlled biological system. Regarding the delay as parameter, we investigate the existence of local Hopf bifurcations. By using the Hassard method and the center manifold argument, we derive the explicit formulas determining the stability,...
In this paper, the time-delayed feedback control method is introduced to stabilize unstable equilibrium points undergoing Hopf bifurcation for an induction motor (IM) drive system. Stability criterion of a nonlinear time-delayed system is first established, and then an effective procedure is shown how to stabilize the unstable equilibrium points by suitably select the feedback gain k and the time-delay...
In this paper, a method is presented and achieved to accurately determine Hopf bifurcation point for an induction motor (IM) drive system, and Hopf bifurcation diagram is showed to indicate evolvement of the equilibrium points from steady state to undergoing Hopf bifurcation and then achieving stabilization again. At last, the classical Floquet theory is applied to confirm the limit cyclepsilas stability.
Aiming at strong nonlinearity and complexity of higher order switching converters, an integrative modeling method was proposed by integrating the state-space average modeling approach with the discrete-time modeling approach, based on which, stability analysis of current-mode controlled higher order switching converters was carried out, and the relation between the stability and the circuit parameters...
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