Phase transitions in networks of chaotic elements with short and long range interactions

Abstract This paper investigates the statistical properties of networks of chaotic elements modeled by coupled map lattices. Transitions separating statistically stable and periodic phases are numerically observed in generic models of excitable media. Similar transitions are studied analytically in lattices of piecewise expanding maps by considering the spectral properties of the Perron-Frobenius operator using the theory of functions of bounded variation in R n.

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