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New family of 4-D hyperchaotic and chaotic systems with quadric surfaces of equilibria

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  • Singh, Jay Prakash
  • Roy, Binoy Krishna
  • Jafari, Sajad

Abstract

This paper reports 4-D hyperchaotic and chaotic systems with various quadric surfaces of equilibria. A known and systematic search procedure is used to generate the proposed systems. Six cases have non-degenerate quadric surfaces (ellipsoid, spheroid, sphere, elliptic hyperboloid of one sheet, circular hyperboloid of one sheet) type of equilibria and two cases have degenerate quadric surfaces (elliptic cylinder, circular cylinder) type of equilibria. All the cases in the new systems have coexistence of chaotic attractors. Chaotic natures of the new systems are confirmed by using various numerical tools. MATLAB simulation results are further validated by circuit implementations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:106:y:2018:i:c:p:243-257
    DOI: 10.1016/j.chaos.2017.11.030
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    References listed on IDEAS

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    5. Singh, Jay Prakash & Roy, B.K., 2016. "The nature of Lyapunov exponents is (+, +, −, −). Is it a hyperchaotic system?," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 73-85.
    6. 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.
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    Cited by:

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    2. Zhou, Ling & You, Zhenzhen & Tang, Yun, 2021. "A new chaotic system with nested coexisting multiple attractors and riddled basins," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    3. Fan, Chunlei & Ding, Qun, 2023. "Design and geometric control of polynomial chaotic maps with any desired positive Lyapunov exponents," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    4. Xiaofei Zhou & Junmei Li & Yulan Wang & Wei Zhang, 2019. "Numerical Simulation of a Class of Hyperchaotic System Using Barycentric Lagrange Interpolation Collocation Method," Complexity, Hindawi, vol. 2019, pages 1-13, February.
    5. Nazarimehr, Fahimeh & Rajagopal, Karthikeyan & Khalaf, Abdul Jalil M. & Alsaedi, Ahmed & Pham, Viet-Thanh & Hayat, Tasawar, 2018. "Investigation of dynamical properties in a chaotic flow with one unstable equilibrium: Circuit design and entropy analysis," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 7-13.

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