New type of intermittency in discontinuous maps

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Abstract
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 〈l〉 on the control parameter ε, in contrast to the three conventional types of intermittency characterized by power-law scaling. Analytical considerations give the relation 〈l〉=log(ε)/log(s)+β (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.