Multistable Systems with Hidden and Self-Excited Scroll Attractors Generated via Piecewise Linear Systems
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 ℝ3 with an even number of equilibria. The design of multistable systems with hidden attractors re...
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Series: | Complexity |
Online Access: | http://dx.doi.org/10.1155/2020/7832489 |
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doaj-32f53c1d79bb490399ad523d9fe330322020-11-25T02:11:12ZengHindawi-WileyComplexity1076-27871099-05262020-01-01202010.1155/2020/78324897832489Multistable Systems with Hidden and Self-Excited Scroll Attractors Generated via Piecewise Linear SystemsR. J. Escalante-González0Eric Campos1Division 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, MexicoDivision 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, MexicoIn 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 ℝ3 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.http://dx.doi.org/10.1155/2020/7832489 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
R. J. Escalante-González Eric Campos |
spellingShingle |
R. J. Escalante-González Eric Campos Multistable Systems with Hidden and Self-Excited Scroll Attractors Generated via Piecewise Linear Systems Complexity |
author_facet |
R. J. Escalante-González Eric Campos |
author_sort |
R. J. Escalante-González |
title |
Multistable Systems with Hidden and Self-Excited Scroll Attractors Generated via Piecewise Linear Systems |
title_short |
Multistable Systems with Hidden and Self-Excited Scroll Attractors Generated via Piecewise Linear Systems |
title_full |
Multistable Systems with Hidden and Self-Excited Scroll Attractors Generated via Piecewise Linear Systems |
title_fullStr |
Multistable Systems with Hidden and Self-Excited Scroll Attractors Generated via Piecewise Linear Systems |
title_full_unstemmed |
Multistable Systems with Hidden and Self-Excited Scroll Attractors Generated via Piecewise Linear Systems |
title_sort |
multistable systems with hidden and self-excited scroll attractors generated via piecewise linear systems |
publisher |
Hindawi-Wiley |
series |
Complexity |
issn |
1076-2787 1099-0526 |
publishDate |
2020-01-01 |
description |
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 ℝ3 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. |
url |
http://dx.doi.org/10.1155/2020/7832489 |
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1715551392705282048 |