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Five new 4-D autonomous conservative chaotic systems with various type of non-hyperbolic and lines of equilibria

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  • Singh, Jay Prakash
  • Roy, Binoy Krishna

Abstract

Very little research is available in the field of 4-D autonomous conservative chaotic systems. This paper presents five new 4-D autonomous conservative chaotic systems having non-hyperbolic equilibria with various characteristics. The proposed systems have different numbers of non-hyperbolic equilibrium points. One of the new systems has four non-hyperbolic equilibria points along with lines of equilibria. Hence, this system may belong to the category of hidden attractors chaotic system. The first, second, fourth and fifth type of the systems exhibit coexistence of chaotic flow, whereas the third type of the system exhibits coexistence of chaotic flows with quasi-periodic behaviour. The chaotic behaviours of the proposed systems are verified by using phase portrait plot, Poincaré map, local Lyapunov spectrum, bifurcation diagram and frequency spectrum plots. The conservative nature of the proposed systems is proved by finding the sum of finite-time local Lyapunov exponents, finite-time local Lyapunov dimensions and divergence of the vector field. The sum of the finite-time local Lyapunov exponents and divergence of the vector field are equal to zero, and local Lyapunov dimension is equal to the order of the system confirm the conservative nature of the new chaotic systems.

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  • 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.
    • Handle: RePEc:eee:chsofr:v:114:y:2018:i:c:p:81-91
    DOI: 10.1016/j.chaos.2018.07.001
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    Cited by:

    1. Jia, Hongyan & Shi, Wenxin & Wang, Lei & Qi, Guoyuan, 2020. "Energy analysis of Sprott-A system and generation of a new Hamiltonian conservative chaotic system with coexisting hidden attractors," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    2. Li, Chunbiao & Sprott, Julien Clinton & Zhang, Xin & Chai, Lin & Liu, Zuohua, 2022. "Constructing conditional symmetry in symmetric chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    3. Jia, Hongyan & Liu, Jingwen & Li, Wei & Du, Meng, 2023. "A family of new generalized multi-scroll Hamiltonian conservative chaotic flows on invariant hypersurfaces and FPGA implementation," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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