Dynamical properties of a dissipative discontinuous map: A scaling investigation

Author(s)

Aguilar-Sanchez, R. ^[1] ; Leonel, Edson D. ^[2] ; Mendez-Bermudez, J. A. ^[3]

Affiliation

^[1] Benemerita Univ Autonoma Puebla, Fac Ciencias Quim, Puebla 72570 - Mexico

^[2] UNESP Univ Estadual Paulista, Dept Fis, BR-13506900 Rio Claro, SP - Brazil

^[3] Benemerita Univ Autonoma Puebla, Inst Fis, Puebla 72570 - Mexico

• Document type: Journal article
• Source: Physics Letters A; v. 377, n. 44, p. 3216-3222, DEC 13 2013.
• Web of Science Citations: 1

Abstract

The effects of dissipation on the scaling properties of nonlinear discontinuous maps are investigated by analyzing the behavior of the average squared action < I-2 > as a function of the n-th iteration of the map as well as the parameters K and gamma, controlling nonlinearity and dissipation, respectively. We concentrate our efforts to study the case where the nonlinearity is large; i.e., K >> 1. In this regime and for large initial action I-0 >> K, we prove that dissipation produces an exponential decay for the average action < I >. Also, for I-0 congruent to 0, we describe the behavior of < I-2 > using a scaling function and analytically obtain critical exponents which are used to overlap different curves of < I-2 > onto a universal plot. We complete our study with the analysis of the scaling properties of the deviation around the average action omega. (C) 2013 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 12/23688-5 - Exponents and scaling laws, phase transitions and transport properties of time dependent systems
• Grantee: Edson Denis Leonel
• Support Opportunities: Regular Research Grants