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Bogdanov–Takens Bifurcation in a Shape Memory Alloy Oscillator with Delayed Feedback

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  • Jinbin Wang
  • Lifeng Ma

Abstract

This work is focused on a shape memory alloy oscillator with delayed feedback. The main attention is to investigate the Bogdanov–Takens (B-T) bifurcation by choosing feedback parameters and time delay . The conditions for the occurrence of the B-T bifurcation are derived, and the versal unfolding of the norm forms near the B-T bifurcation point is obtained by using center manifold reduction and normal form. Moreover, it is demonstrated that the system also undergoes different codimension-1 bifurcations, such as saddle-node bifurcation, Hopf bifurcation, and saddle homoclinic bifurcation. Finally, some numerical simulations are given to verify the analytic results.

Suggested Citation

  • Jinbin Wang & Lifeng Ma, 2020. "Bogdanov–Takens Bifurcation in a Shape Memory Alloy Oscillator with Delayed Feedback," Complexity, Hindawi, vol. 2020, pages 1-10, October.
    • Handle: RePEc:hin:complx:9132501
    DOI: 10.1155/2020/9132501
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