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New type of intermittency in discontinuous maps. (English) Zbl 0969.37511
Summary: Intermittent behavior originating in a point of discontinuity in 1D maps is investigated. Studying the duration of the laminar phase, we find a logarithmic dependence of the average laminar length \(\langle l\rangle\) on the control parameter \(\epsilon\) in contrast to the three conventional types of intermittency characterized by power-law scaling. Analytical considerations give the relation \(\langle l\rangle=\log (\epsilon)/\log(s)+\beta\) (where \(s\) is the ‘slope’ at the point of discontinuity). Numerical data obtained from a relaxation oscillator model are in good agreement with these results.

MSC:
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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