Periodic solutions for a four-dimensional hyperchaotic system

[摘要] In this paper, we show a zero-Hopf bifurcation in a four-dimensional smooth quadratic autonomous hyperchaotic system. Using averaging theory, we prove the existence of periodic orbits bifurcating from the zero-Hopf equilibrium located at the origin of the hyperchaotic system, and the stability conditions of periodic solutions are given.

[学科分类] 航空航天科学

[关键词] Hyperchaotic system;Zero-Hopf bifurcation;Periodic solution;Averaging theory