So I have been given a problem describing a system in R^2 using polar coordinates r,theta by
r' = (1 - (1/2)*cos(theta))*(r - r^2) = f(r,theta)
(theta)' = 1 = g(r,theta)
and I'm asked to find a periodic solution r(t), and theta(t) for the system. (for this purpose theta = 2*k*pi , with k is an integer, is identified with theta=0)
I really don't know how to solve it, any help please?
r' = (1 - (1/2)*cos(theta))*(r - r^2) = f(r,theta)
(theta)' = 1 = g(r,theta)
and I'm asked to find a periodic solution r(t), and theta(t) for the system. (for this purpose theta = 2*k*pi , with k is an integer, is identified with theta=0)
I really don't know how to solve it, any help please?