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

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  • R. J. Escalante-González
  • Eric Campos

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 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.

Suggested Citation

  • R. J. Escalante-González & Eric Campos, 2020. "Multistable Systems with Hidden and Self-Excited Scroll Attractors Generated via Piecewise Linear Systems," Complexity, Hindawi, vol. 2020, pages 1-12, April.
    • Handle: RePEc:hin:complx:7832489
    DOI: 10.1155/2020/7832489
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    Cited by:

    1. Prasina Alexander & Selçuk Emiroğlu & Sathiyadevi Kanagaraj & Akif Akgul & Karthikeyan Rajagopal, 2023. "Infinite coexisting attractors in an autonomous hyperchaotic megastable oscillator and linear quadratic regulator-based control and synchronization," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(1), pages 1-13, January.
    2. Azam, Anam & Aqeel, Muhammad & Sunny, Danish Ali, 2022. "Segmented disc dynamo with symmetric multidirectional patterns of multiscroll chaotic attractors," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 108-127.
    3. Barajas-Ramírez, Juan Gonzalo & Franco-López, Arturo & González-Hernández, Hugo G., 2021. "Generating Shilnikov chaos in 3D piecewise linear systems," Applied Mathematics and Computation, Elsevier, vol. 395(C).

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