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

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In this article, we will investigate a retarded van der Pol-Duffing oscillator with multiple delays.At first, we will find conditions for which air force medical technician badge Bogdanov-Takens (B-T) bifurcation occurs around the trivial equilibrium of the proposed system.The center 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 6love luzern those for the Hopf, double limit cycle, homoclinic, saddle-node, and Bogdanov-Takens bifurcation.In order to meet the theoretical requirements, extensive numerical simulations have been presented in the conclusion.