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Anomalous statistics for type-III intermittency. (English) Zbl 0892.58054

Summary: The statistics for the distribution of laminar phases in type-III intermittency is examined for the map \(x_{n+1}= -((1+ \mu)x_n+ x^3_n) e^{-bx^2_n}\). Due to a strongly nonuniform reinjection process, characteristic deviations from the normal statistics are observed. There is an enhancement of relatively long laminar phases followed by an abrupt cut-off of laminar phases beyond a certain length.
The paper also examines the bifurcation structure of two symmetrically coupled maps, each displaying a subcritical period-doubling bifurcation. The conditions for such a pair of coupled maps to exhibit type-II intermittency are discussed.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37G99 Local and nonlocal bifurcation theory for dynamical systems
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