Consider an autonomous ordinary differential equation for x(t) of the form du dt = f(x;p), where pe is a bifurcation par

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Consider An Autonomous Ordinary Differential Equation For X T Of The Form Du Dt F X P Where Pe Is A Bifurcation Par 1 (24.12 KiB) Viewed 21 times

Consider an autonomous ordinary differential equation for x(t) of the form du dt = f(x;p), where pe is a bifurcation parameter and f(x;p) is a function with no explicit dependence in the independent variablet. Suppose there is a bifurcation point at (Tu) = (0,0). Which canonical bifurcation does the following statement describe? • Two critical points for u < 0, one at = u(unstable) and the other at x = 0 (stable). • Two critical points for p > 0, one at <=u (stable) and the other at x = 0 (unstable). O Saddle node O Transcritical O Supercritical pitchfork O Subcritical pitchfork