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Generating chaotic attractors on a surface

Author

Listed:
  • Morel, C.
  • Vlad, R.
  • Morel, J.-Y.
  • Petreus, D.

Abstract

The present paper introduces a new method to generate several independent periodic attractors, based on a switching piecewise-constant controller. We demonstrate here that the state space equidistant repartition of these attractors is on an arbitrarily precise zone of a paraboloid or plane. We determine the state space domains where the attractors are generated from different initial conditions. A mathematical formula giving their maximal number in function of the controller piecewise-constant values is then deduced.

Suggested Citation

  • Morel, C. & Vlad, R. & Morel, J.-Y. & Petreus, D., 2011. "Generating chaotic attractors on a surface," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(11), pages 2549-2563.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:11:p:2549-2563
    DOI: 10.1016/j.matcom.2011.05.003
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    References listed on IDEAS

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    1. Peng, Mingshu, 2005. "Symmetry breaking, bifurcations, periodicity and chaos in the Euler method for a class of delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1287-1297.
    2. Morel, Cristina & Bourcerie, Marc & Chapeau-Blondeau, François, 2005. "Generating independent chaotic attractors by chaos anticontrol in nonlinear circuits," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 541-549.
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    Cited by:

    1. Pham, Viet–Thanh & Jafari, Sajad & Volos, Christos & Kapitaniak, Tomasz, 2016. "A gallery of chaotic systems with an infinite number of equilibrium points," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 58-63.
    2. Morel, C. & Morel, J.-Y. & Danca, M.F., 2018. "Generalization of the Filippov method for systems with a large periodic input," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 146(C), pages 1-13.

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