Periodic solutions for a four-dimensional hyperchaotic system

Abstract

Abstract 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.

Keywords

• Hyperchaotic system
• Zero-Hopf bifurcation
• Periodic solution
• Averaging theory