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Using Routh-Hurwitz criterion and Hopf bifurcation theorem, stability of the equilibrium points and Hopf bi- furcation of coupled van der Pol and Duffing oscillators are investigated. The parametric curve corresponding to Hopf bi- furcation and the existence region for the limit cycle in the parameter space are derived. The method of multiple time scales is used to deduce the analytical approximation of the limit cycle, and the accuracy of the analytical approximation is verified by direct numerical integration.

Hopf Bifurcation Analysis and Approximation of Limit Cycle in Coupled Van Der Pol and Duffing Oscillators