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Multistability, quasiperiodicity and chaos in a self-oscillating ring dynamical system with three degrees of freedom based on the van der Pol generator

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  • Astakhov, Sergey
  • Astakhov, Oleg
  • Fadeeva, Natalia
  • Astakhov, Vladimir

Abstract

In this paper, we consider a self-oscillating ring system consisting of a nonlinear amplifier and a chain of three linear oscillators. The equations for this system are derived and the results of numerical simulations are presented. The inherent regimes of the self-oscillating system are studied versus the control parameters, and the results of bifurcation analysis are described. It was found that the addition of linear oscillators to the feedback loop of the classical van der Pol generator leads to the appearance of quasiperiodic and chaotic regimes, as well as the formation of multistability. The bifurcation mechanism of the multistability formation determined by two supercritical Andronov - Hopf bifurcations of the steady state and the subcritical Neimark - Sacker bifurcation of the saddle limit cycle is revealed. Transitions to chaos are investigated for each family of multistable states. Transition to chaos is observed through a sequence of doubling bifurcations of torus in a wide range of values of the control parameters.

Suggested Citation

  • Astakhov, Sergey & Astakhov, Oleg & Fadeeva, Natalia & Astakhov, Vladimir, 2021. "Multistability, quasiperiodicity and chaos in a self-oscillating ring dynamical system with three degrees of freedom based on the van der Pol generator," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    • Handle: RePEc:eee:chsofr:v:148:y:2021:i:c:s0960077921003325
    DOI: 10.1016/j.chaos.2021.110978
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    Cited by:

    1. Huang, Juanjuan & Bi, Qinsheng, 2023. "Multiple modes of bursting phenomena in a vector field of triple Hopf bifurcation with two time scales," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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