Dynamical properties of a dissipative discontinuous map: A scaling investigation

The effects of dissipation on the scaling properties of nonlinear discontinuous maps are investigated by analyzing the behavior of the average squared action 〈I2〉 as a function of the n-th iteration of the map as well as the parameters K and γ, controlling nonlinearity and dissipation, respectively....

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Bibliographic Details
Published in:Physics letters. A 2013-12, Vol.377 (44), p.3216-3222
Main Authors: Aguilar-Sánchez, R., Leonel, Edson D., Méndez-Bermúdez, J.A.
Format: Article
Language:English
Subjects:
Decay
Deviation
Discontinuous map
Dissipation
Exponents
Mathematical analysis
Nonlinearity
Scaling
Solid state physics
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Summary:The effects of dissipation on the scaling properties of nonlinear discontinuous maps are investigated by analyzing the behavior of the average squared action 〈I2〉 as a function of the n-th iteration of the map as well as the parameters K and γ, 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 I0≫K, we prove that dissipation produces an exponential decay for the average action 〈I〉. Also, for I0≅0, we describe the behavior of 〈I2〉 using a scaling function and analytically obtain critical exponents which are used to overlap different curves of 〈I2〉 onto a universal plot. We complete our study with the analysis of the scaling properties of the deviation around the average action ω. •We study the effects of dissipation on the scaling properties of nonlinear discontinuous maps.•We investigate the behavior of the average squared action as a function of the nonlinearity and dissipation.•We concentrate our efforts to study the case where the nonlinearity is large.•We prove that dissipation produces an exponential decay for the average action.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2013.10.006