Question: 1. Consider the equation below x+(x y)x + x = 0 - (a) Apply the Lienard and Bendixson criteria and explain their consequences. (b)

1. Consider the equation below x+(x y)x + x = 0 -

1. Consider the equation below x+(x y)x + x = 0 - (a) Apply the Lienard and Bendixson criteria and explain their consequences. (b) Consider y as the bifurcation parameter. Show that the system undergoes a Hopf bifurcation and calculate the amplitude of the arising oscillations. (c) Show the behavior by running numerical simulations for different parameter values.

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