Periodic orbits in the hyperchaotic Chen system

TL;DR

This paper investigates the hyperchaotic Chen system, demonstrating a zero-Hopf bifurcation and proving the emergence of two periodic orbits from the equilibria using averaging theory.

Contribution

It introduces the analysis of zero-Hopf bifurcation in the hyperchaotic Chen system and proves the existence of bifurcating periodic orbits with a rigorous mathematical approach.

Findings

Zero-Hopf bifurcation occurs in the hyperchaotic Chen system.

Two periodic orbits bifurcate from the zero-Hopf equilibria.

Averaging theory is used to prove the existence of these orbits.

Abstract

In this work, we show that a zero--Hopf bifurcation take place in the Hyperchaotic Chen system as parameters vary. Using averaging theory, we prove the existence of two periodic orbits bifurcating from the zero--Hopf equilibria located at the origin of the Hyperchaotic Chen system.