Statistical and dynamical properties of a dissipative kicked rotator

Oliveira, Diego F. M.; Leonel, Edson D.

doi:10.1016/j.physa.2014.06.005

Cited by 5 publications

(3 citation statements)

References 41 publications

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“…We start the numerical investigations of DRSM without the presence of noise obtaining the Lyapunov and isoperiodic diagrams for the dissipation parameter γ and relativistic parameter β besides the kicking strength K and in this way we extend the previous investigation performed in Ref. [10]. The birth of period-1 structures in the (K, β) plane was also analytically obtained and numerically corroborated in the Lyapunov and isoperiodic diagrams.…”

Section: Discussionmentioning

confidence: 54%

“…[10], where the authors investigated the statistical and dynamical behaviors for conservative and dissipative relativistic particles in waveguide. In order to understand and to describe the role of dissipation and relativistic parameters in the DRSM we perform extensive numerical investigations besides some few analytical analysis.…”

Section: Introductionmentioning

confidence: 99%

“…In the present work we revisit the investigation of nonlinear dynamics of a particle described by a dissipative relativistic standard map (DRSM), introduced by [5] and later explored in [7,8,9] and, specially extend the study published by Oliveira and Leonel in the Ref. [10], where the authors investigated the statistical and dynamical behaviors for conservative and dissipative relativistic particles in waveguide. In order to understand and to describe the role of dissipation and relativistic parameters in the DRSM we perform extensive numerical investigations besides some few analytical analysis.…”

Section: Introductionmentioning

confidence: 99%

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The effect of temperature on generic stable periodic structures in the parameter space of dissipative relativistic standard map

2017

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Abstract. In this work, we have characterized changes in the dynamics of a two-dimensional relativistic standard map in the presence of dissipation and specially when it is submitted to thermal effects modeled by a Gaussian noise reservoir. By the addition of thermal noise in the dissipative relativistic standard map (DRSM) it is possible to suppress typical stable periodic structures (SPSs) embedded in the chaotic domains of parameter space for large enough temperature strengths. Smaller SPSs are first affected by thermal effects, starting from their borders, as a function of temperature. To estimate the necessary temperature strength capable to destroy those SPSs we use the largest Lyapunov exponent to obtain the critical temperature (TC ) diagrams. For critical temperatures the chaotic behavior takes place with the suppression of periodic motion, although, the temperature strengths considered in this work are not so large to convert the deterministic features of the underlying system into a stochastic ones.

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Section: Discussionmentioning

confidence: 54%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The effect of temperature on generic stable periodic structures in the parameter space of dissipative relativistic standard map

2017

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An investigation of the parameter space in a tri-trophic food chain model with refuge

Kumbhakar,

Hossain,

Karmakar

et al. 2024

Mathematics and Computers in Simulation

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Crises in a dissipative bouncing ball model

et al. 2015

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The dynamics of a bouncing ball model under the influence of dissipation is investigated by using a two dimensional nonlinear mapping. When high dissipation is considered, the dynamics evolves to different attractors. The evolution of the basins of the attracting fixed points is characterized, as we vary the control parameters. Crises between the attractors and their boundaries are observed. We found that the multiple attractors are intertwined, and when the boundary crisis between their stable and unstable manifolds occur, it creates a successive mechanism of destruction for all attractors originated by the sinks. Also, an impact physical crises is setup, and it may be useful as a mechanism to reduce the number of attractors in the system.

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Statistical and dynamical properties of a dissipative kicked rotator

Cited by 5 publications

References 41 publications

The effect of temperature on generic stable periodic structures in the parameter space of dissipative relativistic standard map

The effect of temperature on generic stable periodic structures in the parameter space of dissipative relativistic standard map

An investigation of the parameter space in a tri-trophic food chain model with refuge

Crises in a dissipative bouncing ball model

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