Complex dynamics and Bogdanov-Takens bifurcations in a retarded van der Pol-Duffing oscillator with positional delayed feedback

Complex dynamics and Bogdanov-Takens bifurcations in a retarded van der Pol-Duffing oscillator with positional delayed feedback

Blog Article

In this article, we will investigate a retarded van der Pol-Duffing oscillator with multiple delays.At first, we will find conditions for which Bogdanov-Takens (B-T) bifurcation occurs around the trivial equilibrium of the proposed system.The center kaiser copy stands manifold theory has been used to extract second order normal form of the B-T bifurcation.After that, we derived third order normal form.We also provide a few bifurcation diagrams, including those for the Hopf, double limit cycle, homoclinic, saddle-node, and Bogdanov-Takens bifurcation.

In order to meet the theoretical requirements, tasoliesi extensive numerical simulations have been presented in the conclusion.