dt 2. (a) Consider the one-parameter family of nonlinear ordinary differential equations de = (x - 1)(x - a² +1), where
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dt 2. (a) Consider the one-parameter family of nonlinear ordinary differential equations de = (x - 1)(x - a² +1), where
dt 2. (a) Consider the one-parameter family of nonlinear ordinary differential equations de = (x - 1)(x - a² +1), where a is a real parameter. i. Find all equilibrium points. ii. Sketch the bifurcation diagram, and indicate the behaviour of non- equilibrium solutions using appropriate arrows. iii. Find all bifurcation points and classify them.
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