System of first order equations, Mathematics

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Consider the Van der Pol oscillator

x′′- µ(1 - x2)x′ + x = 0

(a) Write this equation as a system of first order equations

(b) Taking µ = 2, use MatLab's routine ode45 to compute the solution for the initial value problem x(0) = 0 and x′ (0) = 5 from t = 0 to t = 40. Plot x as a function of t and also plot x vs x′ in phase-space.

(c) Repeat for the initial conditions x(0) = 0 and x′ (0) = 0.01.

(d) What is the ?xed point of the system? Use your numerical results to argue what the long time behavior of the system is.


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