A possible mechanism for the self-organization of complex patterns is the selective amplification of some fluctuation modes provided by external noise. This situation is naturally realized if we have a distributed system that undergoes explosive development from some unstable stationary state. A particular example (and one that is very important for applications) is explosive population growth in fluctuating media. We show in this chapter that such growth results in the formation of very complex intermittent patterns, where small regions with greatly enhanced population density randomly alternate with larger regions that are sparsely populated. We shall also investigate the explosion threshold in different types of fluctuating media.
KeywordsStochastic Differential Equation Ignition Time Creation Rate Breeding Center Spherical Spreading
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