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Under general assumptions we give upper bounds, proportional to the volume of the domain, on the temporal and spatial complexity of solutions to systems of reaction-diffusion equations. The notions of complexity measure instantaneous rather than asymptotic complexity, but time averaged versions of the estimates give bounds on entropy and Hausdorff dimension of any attracting set. The techniques involve the use of quantum mechanical estimates to bound the growth rates of small perturbations.
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Kopell et al. (1986) studied this question.
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