Multistable Systems with Hidden and Self-Excited Scroll Attractors Generated via Piecewise Linear Systems

Author:

Escalante-González R. J.1,Campos Eric1ORCID

Affiliation:

1. Division of Applied Mathematics, Institute for Scientific and Technological Research of San Luis Potosí, Camino a la Presa San José 2055, Lomas 4 Sección 78216, San Luis Potosí, Mexico

Abstract

In this work, we present an approach to design a multistable system with one-directional (1D), two-directional (2D), and three-directional (3D) hidden multiscroll attractor by defining a vector field on 3 with an even number of equilibria. The design of multistable systems with hidden attractors remains a challenging task. Current design approaches are not as flexible as those that focus on self-excited attractors. To facilitate a design of hidden multiscroll attractors, we propose an approach that is based on the existence of self-excited double-scroll attractors and switching surfaces whose relationship with the local manifolds associated to the equilibria lead to the appearance of the hidden attractor. The multistable systems produced by the approach could be explored for potential applications in cryptography, since the number of attractors can be increased by design in multiple directions while preserving the hidden attractor allowing a bigger key space.

Funder

Consejo Nacional de Ciencia y Tecnología

Publisher

Hindawi Limited

Subject

Multidisciplinary,General Computer Science

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