Consider the following system of equations: r(t) =x(t) + ay(t)+.r(t)g(t), y(t) = -ay(t) = x(t)y(t). (3)...

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Consider the following system of equations: r(t) =x(t) + ay(t)+.r(t)g(t), y(t) = -ay(t) = x(t)y(t). (3) (a) Set a = 0.1. Find the equilibrium points and determine their stability as a function of B. (b) Plot the phase portrait (x vs y) for the following parameter values 3 (0.25, 0.5, 0.75, 1}. What types of nonlinear behavior do you observe? (c) Learn the concept of a Hopf bifurcation and describe it. Explain the connection with part (b). Consider the following system of equations: r(t) =x(t) + ay(t)+.r(t)g(t), y(t) = -ay(t) = x(t)y(t). (3) (a) Set a = 0.1. Find the equilibrium points and determine their stability as a function of B. (b) Plot the phase portrait (x vs y) for the following parameter values 3 (0.25, 0.5, 0.75, 1}. What types of nonlinear behavior do you observe? (c) Learn the concept of a Hopf bifurcation and describe it. Explain the connection with part (b).