A Monte-Carlo approach to the effect of noise on local stability in polynomial difference equations
We present an analysis of the stability behaviour of a class of one-step difference equations describing an iterated polynomial mapping. Such equations are commonly used to model population dynamics in discrete time. We use Monte-Carlo methods to investigate the effect of a state-dependent random perturbation on the local stability of such equations. In particular we focus on the probability of stability in transitionary initial-value regions; regions where a switch in the qualitative behaviour of the deterministic equation is observed.
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