# Behaviour of $r'=r-r^3 , \theta'=(\sin\theta)^2+a$

What are the local and global behavior of solutions of

$r'=r-r^3$

$\theta'=(\sin\theta)^2+a$

at the bifurcation value $a=-1$?

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What have you done? Are you asking or telling? –  Pragabhava Nov 30 '12 at 0:48
I don't know how to describe the local and global behaviors. –  Max Nov 30 '12 at 1:48
Start by looking at the critical points and limit cycles, and see if they are attractors or not. –  Pragabhava Nov 30 '12 at 1:54
These are the equilibrium points I found: when a>0, no equilibria. when a<0, no equilibria, but when a=0, I have the origin(0,0), (1,0),(1,pi). –  Max Nov 30 '12 at 2:27
Still looking for a solution –  Max Nov 30 '12 at 4:58