Generation of multi-scroll attractors without equilibria via piecewise linear systems

Abstract

"In this paper, we present a new class of dynamical system without equilibria which possesses a multiscroll attractor. It is a piecewise-linear system which is simple, stable, displays chaotic behavior and serves as a model for analogous non-linear systems. We test for chaos using the 0-1 Test for Chaos from Gottwald and Melbourne [SIAM J. Appl. Dyn. Syst. 8(1), 129-145 (2009)]. Piecewise-linear (PWL) systems are switching systems composed of linear affine subsystems along with a rule which determines the acting subsystem. These systems are known to be capable of producing chaotic attractors, as in the well studied Chua's circuit. This paper discusses the generation of multiscroll attractors without equilibria based on PWL systems.