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

Abstract EN

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 A1,2 and time delay τ.

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.