Exponential localization of linear response in networks with exponentially decaying coupling
… As an example of estimation of exponential decay rate and coherence length in a
continuation problem, we consider a two-dimensional network of coupled bistable units with
exponentially decaying coupling. More precisely we take the index set S to be Z2 and the … In
particular if we suppose that at ϵ = 0 all but one of the units are in the same stable equilibrium:
xn = 0 ∀n = 0 and x0 = 1, then this equilibrium, which we will denote by x(0), has a unique
continuation x(ϵ) for ϵ<ϵ0, and they were able to claim for one-dimensional nearest-neighbour …
continuation problem, we consider a two-dimensional network of coupled bistable units with
exponentially decaying coupling. More precisely we take the index set S to be Z2 and the … In
particular if we suppose that at ϵ = 0 all but one of the units are in the same stable equilibrium:
xn = 0 ∀n = 0 and x0 = 1, then this equilibrium, which we will denote by x(0), has a unique
continuation x(ϵ) for ϵ<ϵ0, and they were able to claim for one-dimensional nearest-neighbour …
Abstract
Let S be a countable metric space with metric d, for each let, be Banach spaces, and let X, Y be the subsets of, respectively, with finite supremum norm over their factors. Let be an invertibleexponentially local'bounded linear map, ie such that for some,
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