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Generating Shilnikov chaos in 3D piecewise linear systems

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  • Barajas-Ramírez, Juan Gonzalo
  • Franco-López, Arturo
  • González-Hernández, Hugo G.

Abstract

We propose a construction algorithm that takes advantage of the geometric features of linear eigenspaces with focus-saddle and center-node equilibrium points to construct piecewise linear systems with Shilnikov chaos. Unlike previously published algorithms to generate chaos, we construct homoclinic (heteroclinic) orbits combining hyperbolic and nonhyperbolic domains by appropriately choosing locations where the trajectories move between linear domains through the switching surfaces at their crossing sections. We present two variants of our construction algorithm: On the first, a homoclinic orbit is constructed locating the exit and return points on the crossing section of the switching surface are connected by a nonhyperbolic center-node domain. In the second variant, we extend the construction method to construct heteroclinic loops with two switching surfaces between them. For the resulting systems a wide range of parameter values results on Shilnikov chaos. These chaotic systems are illustrated with numerical simulations.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:395:y:2021:i:c:s0096300320308304
    DOI: 10.1016/j.amc.2020.125877
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    References listed on IDEAS

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    1. 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.
    2. Castro, Jose & Alvarez, Joaquin & Verduzco, Fernando & Palomares-Ruiz, Juan E., 2017. "Chaotic behavior of driven, second-order, piecewise linear systems," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 8-13.
    3. Liu, Xinzhi & Teo, Kok-Lay & Zhang, Hongtao & Chen, Guanrong, 2006. "Switching control of linear systems for generating chaos," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 725-733.
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