Consider the dynamical system

(a) Use linear stability analysis to characterize the steady states in the interval x ∈ [−3.5, 3.5] and y ∈ [−3.5, 3.5]. You are not allowed to use the eigenvalue functions in MATLAB to compute the eigenvalues but you can use this function to check your answer.

(b) Numerically construct a phase plane portrait for the system in part (a) on the interval x ∈ [−3.5, 3.5] and y ∈ [−3.5, 3.5]. Your program should automatically generate the overall phase plane as well as additional figures that zoom in on the different steady states. Use your knowledge of numerical integration and MATLAB to figure out a good way to solve the problem. For each plot for the zooms near the steady state, discuss how the numerical solution compares to the linear stability analysis.

Transcribed Image Text:

d X # [³] = [ dt y xy + sin лy x(y² - 1) ]