Hopf bifurcation analysis of some hyperchaotic systems with time-delay controllers. (English) Zbl 1145.93361
Summary: A four-dimensional hyperchaotic Lü system with multiple time-delay controllers is considered in this paper. Based on the theory of Hopf bifurcation in delay system, we obtain a simple relationship between the parameters when the system has a periodic solution. Numerical simulations show that the assumption is a rational condition, choosing parameter in the determined region can control hyperchaotic Lü system well, the chaotic state is transformed to the periodic orbit. Finally, we consider the differences between the analysis of the hyperchaotic Lorenz system, hyperchaotic Chen system and hyperchaotic Lü system.
MSC:
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
Keywords:
Hopf bifurcation; periodic solution; multiple delays and parameters; hyperchaotic Lü system; hyperchaotic Chen system; hyperchaotic Lorenz systemReferences:
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