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A gallery of chaotic systems with an infinite number of equilibrium points

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  • Pham, Viet–Thanh
  • Jafari, Sajad
  • Volos, Christos
  • Kapitaniak, Tomasz

Abstract

In this work, a systematic search for finding chaotic systems with infinite equilibria is described. As a result, we obtained a gallery of chaotic systems with various shapes of equilibrium points such as a line, two parallel lines, a piece–wise linear curve, a parabola, a hyperbola, or a circle. Interestingly, such novel systems exhibit “hidden attractors”, which play vital roles in nonlinear theory and practical engineering issues.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:93:y:2016:i:c:p:58-63
    DOI: 10.1016/j.chaos.2016.10.002
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    Cited by:

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    4. Singh, Jay Prakash & Roy, Binoy Krishna, 2018. "Five new 4-D autonomous conservative chaotic systems with various type of non-hyperbolic and lines of equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 81-91.
    5. Lai, Qiang & Norouzi, Benyamin & Liu, Feng, 2018. "Dynamic analysis, circuit realization, control design and image encryption application of an extended Lü system with coexisting attractors," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 230-245.
    6. Singh, Jay Prakash & Roy, Binoy Krishna & Jafari, Sajad, 2018. "New family of 4-D hyperchaotic and chaotic systems with quadric surfaces of equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 243-257.

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