The author gives the following new definitions of the stability of ordinary differential equations. Given a vector field v on an oriented manifold X and given \(\epsilon >0\), let u be the steady state of the Fokker-Planck equation for v with \(\epsilon\)-diffusion. Existence, uniqueness and global attraction of u is proved when X is compact. Vector fields are said to be equivalent or stable according to whether their steady states are. A similar theory is developed for diffeomorphism. The author shows that this new defintion has a number of advantages over structural stability, especially it is shown that stable systems are dense, and that most strange attractors are stable, including non- hyperbolic ones.