Heteroclinic, Homoclinic and Closed Orbits in the Chen System

Abstract

Bounded orbits such as closed, homoclinic and heteroclinic orbits are discussed in this work for a Lorenz-like 3D nonlinear system. For a large spectrum of the parameters, the system has neither closed nor homoclinic orbits but has exactly two heteroclinic orbits, while under other constraints the system has symmetrical homoclinic orbits.