×

Impulsive control and Hopf bifurcation of a new three-dimensional chaotic system. (Chinese. English summary) Zbl 1299.37034

Summary: The issues of impulsive stabilization and the dynamic behavior of a new three-dimensional chaotic system are investigated. Using a Lyapunov function, the stabilization of the chaotic system is discussed. This paper derives some sufficient conditions for the stabilization of the system via impulsive control. It is shown that the origin is an equilibrium. From the point of view of normal form theory, the origin is a weak center. Using the first Lyapunov number, it is proved that the system undergoes a sub-critical Hopf bifurcation and hence a unique unstable limit cycle exists under certain conditions. Finally, numerical examples are given to support the analytic results.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C23 Bifurcation theory for ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
37N35 Dynamical systems in control
34A37 Ordinary differential equations with impulses
PDFBibTeX XMLCite
Full Text: DOI