Bifurcations, relaxation time, and critical exponents in a dissipative or conservative Fermi model

We investigated the time evolution for the stationary state at different bifurcations of a dissipative version of the Fermi-Ulam accelerator model. For local bifurcations, as period-doubling bifurcations, the convergence to the inactive state is made using a homogeneous and generalized function at t...

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Veröffentlicht in:Chaos (Woodbury, N.Y.) N.Y.), 2023-02, Vol.33 (2), p.023138-023138
Hauptverfasser: S Rando, Danilo, C Martí, Arturo, D Leonel, Edson
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C Martí, Arturo
D Leonel, Edson
description We investigated the time evolution for the stationary state at different bifurcations of a dissipative version of the Fermi-Ulam accelerator model. For local bifurcations, as period-doubling bifurcations, the convergence to the inactive state is made using a homogeneous and generalized function at the bifurcation parameter. It leads to a set of three critical exponents that are universal for such bifurcation. Near bifurcation, an exponential decay describes convergence whose relaxation time is characterized by a power law. For global bifurcation, as noticed for a boundary crisis, where a chaotic transient suddenly replaces a chaotic attractor after a tiny change of control parameters, the survival probability is described by an exponential decay whose transient time is given by a power law.
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subjects Bifurcations
Convergence
Decay
Dissipation
Exponents
Mathematical models
Parameters
Power law
Relaxation time
title Bifurcations, relaxation time, and critical exponents in a dissipative or conservative Fermi model
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