Analysis of a New Three-Dimensional Quadratic Chaotic System

Abstract

This paper has reported the finding of a new simple three dimensional quadratic chaotic system with three nonlinearities obtained by adding a cross-product nonlinear term to the first equation of the Lu system. Basic properties of the system have been analyzed by means of Lyapunov exponent spectrum and bifurcation diagram of an associated Poincare map. This analysis shows that the system has complex dynamics with some interesting characteristics in which there are several periodic regions, but each of them has quite different periodic orbits. Shilnikov's criterion is included and discussed.

Keywords

• New chaotic attractors
• three quadratic nonlinearities
• modified Lu system
• Lyapunov exponent spectrum
• bifurcation diagram
• Poincare map