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) Outdoor Rocking Arm Chair (Set of 2) 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 Bookshelf 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, extensive numerical simulations have been presented in the conclusion.