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Analysis of three types of initial offset-boosting behavior for a new fractional-order dynamical system

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  • Gu, Shuangquan
  • He, Shaobo
  • Wang, Huihai
  • Du, Baoxiang

Abstract

In this study, a new fractional-order chaotic system is proposed based on the Adomian decomposition method (ADM). The system is proved to have no equilibrium point, so the system has hidden nonlinear characteristics. Furthermore, the initial-offset boosting behavior can be observed from this system. When the system parameters are fixed and the initial value changes, the evolution of the conservative, quasi-conservative, and dissipative phase trajectory boosts are analyzed in detail by numerical simulations, such as phase diagrams, mean values of the state variables, bifurcation diagrams, and dynamical distribution maps. These dynamic behaviors also indicate that the system has striking hidden multistability. Although some chaotic systems with initial-offset boosting behavior has been previously reported, it should be noted that this non-equilibrium fractional-order chaotic system with three types of offset-boosted control of initial value is the first to build and study. Finally, a circuit implementation on a digital signal processor (DSP) demonstrates the validity of the numerical analysis and the physical implementability of the system.

Suggested Citation

  • Gu, Shuangquan & He, Shaobo & Wang, Huihai & Du, Baoxiang, 2021. "Analysis of three types of initial offset-boosting behavior for a new fractional-order dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920310043
    DOI: 10.1016/j.chaos.2020.110613
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    2. Zhenggang Guo & Junjie Wen & Jun Mou, 2022. "Dynamic Analysis and DSP Implementation of Memristor Chaotic Systems with Multiple Forms of Hidden Attractors," Mathematics, MDPI, vol. 11(1), pages 1-13, December.
    3. Yuan, Fang & Xing, Guibin & Deng, Yue, 2023. "Flexible cascade and parallel operations of discrete memristor," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    4. Lin, Hairong & Wang, Chunhua & Du, Sichun & Yao, Wei & Sun, Yichuang, 2023. "A family of memristive multibutterfly chaotic systems with multidirectional initial-based offset boosting," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    5. Zandi-Mehran, Nazanin & Nazarimehr, Fahimeh & Rajagopal, Karthikeyan & Ghosh, Dibakar & Jafari, Sajad & Chen, Guanrong, 2022. "FFT bifurcation: A tool for spectrum analyzing of dynamical systems," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    6. Ahmed A. Abd El-Latif & Janarthanan Ramadoss & Bassem Abd-El-Atty & Hany S. Khalifa & Fahimeh Nazarimehr, 2022. "A Novel Chaos-Based Cryptography Algorithm and Its Performance Analysis," Mathematics, MDPI, vol. 10(14), pages 1-22, July.
    7. Hairong Lin & Chunhua Wang & Fei Yu & Jingru Sun & Sichun Du & Zekun Deng & Quanli Deng, 2023. "A Review of Chaotic Systems Based on Memristive Hopfield Neural Networks," Mathematics, MDPI, vol. 11(6), pages 1-18, March.
    8. Lin, Hairong & Wang, Chunhua & Sun, Jingru & Zhang, Xin & Sun, Yichuang & Iu, Herbert H.C., 2023. "Memristor-coupled asymmetric neural networks: Bionic modeling, chaotic dynamics analysis and encryption application," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

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