Abstract
The dynamics of a unidirectional nonlinear delayed-coupling chaos system is investigated. Based on the local Hopf bifurcation at the zero equilibrium, we prove the global existence of periodic solutions using a global Hopf bifurcation result due to Wu and a Bendixson’s criterion for higher dimensional ordinary differential equations due to Li & Muldowney.
Highlights
We present some preliminary results of system (2) about the existence of local periodic solutions
This is the basis of the global Hopf bifurcation
(H3) is correct, and we show large amplitude periodic solutions exist for values of τ far away from τ1 (0)
Summary
(2016) Global Existence of Periodic Solutions in a Nonlinear Delay-Coupling Chaos System. It has formed a number of chaos control methods, such as the OGY method [3], variational parameter control [4], state feedback control [5], adaptive control [6], optimal control [7], robust control [8] and non-feedback control [9]. In order to understand the ultimate effect of chaos control and synchronization, we need to know the dynamic behavior of original system, and need to discuss the one of new coupled system (see [14]-[18]).
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