Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1897735 | Physica D: Nonlinear Phenomena | 2008 | 10 Pages |
Abstract
We present a bifurcation theory of smooth stochastic dynamical systems that are governed by everywhere positive transition densities. The local dependence structure of the unique strictly stationary evolution of such a system can be expressed by the ratio of joint and marginal probability densities; this ‘dependence ratio’ is a geometric invariant of the system. By introducing an equivalence relation defined on these dependence ratios, we arrive at a bifurcation theory for which in the compact case, the set of stable, i.e. non-bifurcating, systems is open and dense. The theory is illustrated with some simple examples.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
C.G.H. Diks, F.O.O. Wagener,