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In this paper, we consider the well-known Vallis model for El Niño driven by an external excitation. The bifurcation studies on the driven Vallis model are conducted with different control parameters. Then we discuss about the taming of the Hopf bifurcation by varying the driving function. We could note that the system changes its state from stable steady state to oscillatory state and vice versa which is achieved by changing the driving function. Finally, two parameter bifurcation plots are derived to show that impact of the driving function on the system bifurcation points.

Taming of the Hopf bifurcation in a driven El Niño model