Analysis of a class of complex system without equilibria via switched control law

Abstract

"In this article we introduce a new class of complex system without equilibria which exhibits a chaotic multiscroll attractor in each node. The number of scrolls in the attractor is determined by a switched control law to allow the operation of different linear affine systems. Thus, the system is composed of many subsystems which interact with each other to generate a multiscroll attractor. This new class of piecewise linear (PWL) system presents no positive real part in the eigenvalues of the Jacobian matrix as opposed to the reported systems with multiscrolls. The scrolls present a complex behavior since these don’t unwrap and don’t appear close to an unstable manifold of a saddle-focus equilibrium point. A particular case is taken as case study and simulation plots of the attractor are provided.