Highly Complex Chaotic System with Piecewise Linear Nonlinearity and Compound Structures

Abstract

A new chaotic system is presented using a single parameter for a two-scroll attractor with high complexity, high chaoticity and widely chaotic range. The system employs two quadratic nonlinearities and two piecewise-linear nonlinearities. The high chaoticity is measured by the the maximum Lyapunov Exponent of 0.429 and the high complexity is measured by the Kaplan-Yorke dimension of 2.3004. Dynamic properties are described in terms of symmetry, a dissipative system, an existence of attractor, equilibria, Jacobian matrices, bifurcations, Poincaroe maps, chaotic waveforms, chaotic spectrum, and forming mechanisms of compound structures .