ANALYTICAL PROCESS FOR DETERMINATION OF HOPF BIFURCATIONS
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Abstract
In this paper we consider a two dimensional model of the type
dx/dt=bx2 -x2-xy, dy/dt=xy-ay
where a and b are tunable parameters. The Hopf bifurcation theorem provides a powerful analytical tool for exploring properties of periodic solutions of ordinary differential equations [2]. We have used this theorem [1, 4, and 12] for the determination of Hopf bifurcations in nonlinear differential equations and finally applied to show the existence of supercritical and subcritical Hopf bifurcations with some snapshots of periodic oscillations in our model.
Keywords: Limit Cycles, Periodic oscillation, Hopf bifurcation, Subcritical and Supercritical Hopf bifurcation
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