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Dynamics and Complexity Analysis of Fractional-Order Chaotic Systems with Line Equilibrium Based on Adomian Decomposition

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  • Heng Chen
  • Tengfei Lei
  • Su Lu
  • WenPeng Dai
  • Lijun Qiu
  • Lin Zhong

Abstract

In this paper, the Adomian decomposition method (ADM) is applied to solve the fractional-order system with line equilibrium. The dynamics of the system is analyzed by means of the Lyapunov exponent spectrum, bifurcations, chaotic attractor, and largest Lyapunov exponent diagram. At the same time, through the Lyapunov exponent spectrum and bifurcation graph of the system under the change of the initial value, the influence of fractional order q on the system state can be observed. That is, integer-order systems do not have the phenomenon of attractors coexistence, while fractional-order systems have it.

Suggested Citation

  • Heng Chen & Tengfei Lei & Su Lu & WenPeng Dai & Lijun Qiu & Lin Zhong, 2020. "Dynamics and Complexity Analysis of Fractional-Order Chaotic Systems with Line Equilibrium Based on Adomian Decomposition," Complexity, Hindawi, vol. 2020, pages 1-13, October.
    • Handle: RePEc:hin:complx:5710765
    DOI: 10.1155/2020/5710765
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    Cited by:

    1. Jose-Cruz Nuñez-Perez & Vincent-Ademola Adeyemi & Yuma Sandoval-Ibarra & Francisco-Javier Perez-Pinal & Esteban Tlelo-Cuautle, 2021. "Maximizing the Chaotic Behavior of Fractional Order Chen System by Evolutionary Algorithms," Mathematics, MDPI, vol. 9(11), pages 1-22, May.
    2. Wang, Jieyang & Mou, Jun & Xiong, Li & Zhang, Yingqian & Cao, Yinghong, 2021. "Fractional-order design of a novel non-autonomous laser chaotic system with compound nonlinearity and its circuit realization," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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