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Physics Letters A, 66, 035201(R) (2002). Decelerating defects and non-ergodic critical behaviour in a unidirectionally coupled map latticePeter Ashwin(1) Rob Sturman(2).(1) School of Mathematical Sciences, Laver Building, University of Exeter, Exeter EX4 4QE, UK (2) Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, UK Abstract. We examine a coupled map lattice (CML) consisting of an infinite chain of logistic maps coupled in one direction by inhibitory coupling. We find that for sufficiently strong coupling strength there are dynamical states with `decelerating defects', where defects between stable patterns (with chaotic temporal evolution and average spatial period two) slow down but never stop. These defects annihilate each other when they meet. We show for certain states that this leads to a lack of convergence (non-ergodicity) of averages taken from observables in the system and conjecture that this is typical for these states. Link to this paper
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