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Dynamic analysis of piecewise nonlinear systems with fractional differential delay feedback control

Author

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  • Wang, Mei-Qi
  • Ma, Wen-Li
  • Li, Yuan
  • Chen, En-Li
  • Liu, Peng-Fei
  • Zhang, Ming-Zhi

Abstract

This paper mainly analyzes a class of piecewise nonlinear systems with fractional differential delay feedback control. The average method is used to solve the nonlinear system to obtain the amplitude-frequency relationship of the system. The analytical solution of the system can quantitatively analyze the system. At the same time, the correctness of the analytical solution of the system is verified by numerical solution. The effects of linear damping, linear stiffness and nonlinear stiffness of the system and the proportion, fractional order coefficient and fractional order number of the feedback controller on the amplitude-frequency characteristics of the system are analyzed. Finally, the dynamic analysis of the system is carried out. Taking the fractional order coefficient as the bifurcation parameter, the global characteristics of the bifurcation diagram, time history diagram and phase diagram system under different parameter perturbations are studied by power series expansion method. It is found that the system exhibits periodic motion, period doubling motion and chaos with the change of perturbation parameters.

Suggested Citation

  • Wang, Mei-Qi & Ma, Wen-Li & Li, Yuan & Chen, En-Li & Liu, Peng-Fei & Zhang, Ming-Zhi, 2022. "Dynamic analysis of piecewise nonlinear systems with fractional differential delay feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008050
    DOI: 10.1016/j.chaos.2022.112624
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    References listed on IDEAS

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    1. Zhang, Qianhong & Luo, Wei, 2009. "Global exponential stability of fuzzy BAM neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2239-2245.
    2. Li, Kelin & Zhang, Xinhua & Li, Zuoan, 2009. "Global exponential stability of impulsive cellular neural networks with time-varying and distributed delay," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1427-1434.
    3. Satyam Paul & Wen Yu & Xiaoou Li, 2018. "Bidirectional active control of structures with type-2 fuzzy PD and PID," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(4), pages 766-782, March.
    4. Giresse, Tene Alain & Crépin, Kofane Timoleon, 2017. "Chaos generalized synchronization of coupled Mathieu-Van der Pol and coupled Duffing-Van der Pol systems using fractional order-derivative," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 88-100.
    5. Ji, J.C. & Hansen, C.H., 2006. "Stability and dynamics of a controlled van der Pol–Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 555-570.
    6. Zhang, Qiang & Wei, Xiaopeng & Xu, Jin, 2009. "Global exponential stability for nonautonomous cellular neural networks with unbounded delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1144-1151.
    7. Nailu Li & Hua Yang & Anle Mu, 2019. "Improved Grey Particle Swarm Optimization and New Luus-Jaakola Hybrid Algorithm Optimized IMC-PID Controller for Diverse Wing Vibration Systems," Complexity, Hindawi, vol. 2019, pages 1-21, December.
    8. Mathiyalagan, Kalidass & Sangeetha, G., 2020. "Second-order sliding mode control for nonlinear fractional-order systems," Applied Mathematics and Computation, Elsevier, vol. 383(C).
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