A three-dimensional dissipative map modeling type-II intermittency

Abstract

A three-dimensional Poincaré map model for type-II intermittency is proposed. The purpose is to describe this transition in minimal dimension which in turn affects the degree of structural stability of the scenario. This scenario is understood in terms of the interaction of a local subcritical Hopf bifurcation and a global homoclinic bifurcation. The Pomeau-Manneville picture is revisited in order to account for the one-dimensional homoclinic reinjection process. The distribution of the lengths of the laminar episodes is investigated and numerical results are shown to corroborate the theoretical predictions. The influence of noise on type-II intermittency is discussed. The difference between additive and multiplicative noise is emphasized