In this esp ltd sd-2 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 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 danessa myricks soulmate cycle, homoclinic, saddle-node, and Bogdanov-Takens bifurcation.In order to meet the theoretical requirements, extensive numerical simulations have been presented in the conclusion.