Anomalous Statistics for Type-III Intermittency

Abstract

The statistics for the distribution of laminar phases in type-III intermittency is examined for the map $$x_{n+1}=-\left( {(1+\mu )x_n+x_n^3} \right)e^{-bx_n^2}$$. 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.