Stochastic Bifurcations in a Generic Dynamical System: A Qualitative Analysis
One of the main problems in the analysis of nonlinear dynamical systems is the study of the number and stability of the stationary solutions. In a first approach one assumes deterministic conditions, such that all the parameters involved in the problem have fixed values. If this is the case, bifurcation theory1–3 provides the necessary mathematical tools to handle the problem. In many practical situations, however, the restriction of constant parameters is difficult to maintain, and one would like to be able to extend the precise results of bifurcation theory to, for instance, the case in which the bifurcation parameter fluctuates around a well defined mean value.
KeywordsBifurcation Diagram Stochastic Differential Equation Bifurcation Point Stochastic System Bifurcation Parameter
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