Some characteristics of the M function methodology to describe the reinjection process in chaotic intermittency

The M function methodology allows calculating the statistical properties of intermittency in a broad class of one-dimensional maps. It has shown to be very accurate in type I, II, III and V intermittencies; and it also includes the uniform reinjection as a particular case. This paper studies some properties of the M function methodology. We establish the conditions that a reinjection probability density function must verify to obtain and we describe new pathological cases where the reinjection is not uniform, but the characteristic relation is the same that for uniform reinjection.Fil: Elaskar, Sergio Amado. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Estudios Avanzados en Ingeniería y Tecnología. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Estudios Avanzados en Ingeniería y Tecnología; ArgentinaFil: del Rio, Ezequiel(EXT). Universidad Politécnica de Madrid; EspañaFil: Gutierrez Marcantoni, Luis Felipe. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales. Departamento de Aeronáutica; Argentin

Type-I intermittency with discontinuous reinjection probability density in a truncation model of the derivative nonlinear Schrödinger equation

In previous papers, the type-I intermittent phenomenon with continuous reinjection probability density (RPD) has been extensively studied. However, in this paper type-I intermittency considering discontinuous RPD function in one-dimensional maps is analyzed. To carry out the present study the analytic approximation presented by del Río and Elaskar (Int. J. Bifurc. Chaos 20:1185-1191, 2010) and Elaskar et al. (Physica A. 390:2759-2768, 2011) is extended to consider discontinuous RPD functions. The results of this analysis show that the characteristic relation only depends on the position of the lower bound of reinjection (LBR), therefore for the LBR below the tangent point the relation {Mathematical expression}, where {Mathematical expression} is the control parameter, remains robust regardless the form of the RPD, although the average of the laminar phases {Mathematical expression} can change. Finally, the study of discontinuous RPD for type-I intermittency which occurs in a three-wave truncation model for the derivative nonlinear Schrodinger equation is presented. In all tests the theoretical results properly verify the numerical dat