Strange Attractors in a Three-Dimensional Autonomous Polynomial Equation

Abstract

We studied a three-dimensional autonomous polynomial equation. This equation is with a parameter, which we denote as μ. At μ = 0, the system has two saddles, the stable and unstable manifolds of which coincide. We present a comprehensive study on the dynamics of the system for small μ ≠ 0 in a small neighborhood of the unperturbed stable and unstable manifolds, where one of the heteroclinic connections of the two saddles are broken by small perturbations and strange attractors are created.