FLUCTUATIONS IN SYSTEMS WITH MULTIPLE STEADY STATES. APPLICATION TO LANCHESTER EQUATIONS

Abstract : We consider the effects of small random perturbations on deterministic systems of differential equations. The systems of interest have a steady state that is a saddle point. A first exit problem is formulated. The quantity of basic interest is the probability of exit from a band around the deterministic separatrix through a specified boundary, conditioned on initial position. A technique for the approximate calculation of this probability is given. As an example, we show how the theory applies to the calculation of the probability of victory in a combat that has a stochastic component. (Author)

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