Generating extremely multistable systems based on Lurie form systems

Abstract

Chaotic signals and systems are widely used in image encryption, secure communications, weak signal detection and radar systems. In recent years, many researchers have focused on the design of systems that have an infinite number of coexisting chaotic attractors. In this article, we propose some approaches to generating self-reproducing systems with an infinite number of coexisting self-excited or hidden chaotic attractors with the same Lyapunov exponents, based on mathematical models of systems in Lurie form. The proposed approach makes it possible to generate extremely multistable systems, using numerous well-known examples of the existence of chaotic attractors in systems in Lurie form and without resorting to exhaustive computer search. Illustrating the methods proposed in the paper, we construct, in particular, extremely multistable systems with a 1-D and 2-D grid of hidden chaotic attractors using the generalized Chua system, in which the hidden attractors were first discovered by G. А. Leonov and N. V. Kuznetsov.