# Math Help - Number of isolated equilibria

1. ## Number of isolated equilibria

Hi
Suppose for a dynamical system $\dot x = f(x), x \in \mathbb R^n$ there exists a finite number of isolated equilibria, all of them are locally stable (i.e eigenvalues of the associated Jacobian for each equilibrium have negative real parts).
My question is: Can the number of the of equilibria in the statement above exceed one? (sorry if it is a trivial question)

Regards

2. ## Re: Number of isolated equilibria

No. If p and q are two locally stable equilibria, there must exist a locally unstable equilibrium some where "between" them (lying on some curve from one to the other.)

3. ## Re: Number of isolated equilibria

thanks for participation but can you provide a proof or a reference to a proof ?