Introduction and synchronization of a five-term chaotic system with an absolute-value term

Abstract

We propose a new chaotic system that consists of only five terms, including one multiplier and one quadratic term, and one absolute-value term. It is observed that the absolute-value term results in intensifying chaoticity and complexity. The characteristics of the proposed system are investigated by theoretical and numerical tools such as equilibria, stability, Lyapunov exponents, Kaplan-Yorke dimension, frequency spectrum, Poincar, maps, and bifurcation diagrams. The existence of homoclinic and heteroclinic orbits of the proposed system is also studied by a theoretical analysis. Furthermore, synchronization of this system is achieved with a simple technique proposed by Kim et al. (Nonlinear Dyn., 2013, in press) for a practical application.