In this chapter the conditioning method is introduced. The core of the approach is to examine the behaviour of a stochastic system in the SDE framework under the condition that its trajectories are confined to the slow subspace of the deterministic version of the system. A similar procedure has been applied in previous works in the analysis of noise induced speciation [11, 12]. Inspired by this success, the method is generalised here for applications to a broader range of systems. I also highlight how the method can be especially useful in some specific instances. Because a static description of the slow subspace is used (as opposed to a stochastic description, as in Eq. (2.86)), the method is applicable to a broader range of systems than the direct elimination procedure or the Haken slaving principle. Moreover, the procedure is mathematically explicit, straightforward to apply, and addresses the effect of correlated noise terms. One also gains a sense of physical intuition as to the behaviour of the system, which is arguably not present in the FPE setting.
Slow Manifold Stochastic Fluctuation Conditioning Method Endemic State Periodic Vector
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L. Arnold, Random Dynamical Systems, Springer Monographs in Mathematics (Springer, Berlin, 2003)Google Scholar