A family of dissipative two-dimensional mappings: Chaotic, regular and steady state dynamics investigation

Kuwana, Célia Mayumi; Oliveira, Juliano A. de; Leonel, Edson D.

doi:10.1016/j.physa.2013.10.032

Cited by 5 publications

(2 citation statements)

References 26 publications

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“…There are rich dynamic behaviors in some cases, such as in sheared suspensions [11], in creeping flow [12], and around a weakly-magnetized Schwarzschild black hole [13]. This shows that the particle motion becomes complex because of the existence of external force, and the particle system has different dynamic behaviors under different external forces [14][15][16]. Here, we assume that a particle with unit mass is moving on a horizontal smooth plane (p, q), and the forces on the particle in p and q direction are F p and F q , respectively, where:…”

Section: Modelmentioning

confidence: 99%

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Dynamic Analysis of a Particle Motion System

Cui

2018

Mathematics

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This paper formulates a new particle motion system. The dynamic behaviors of the system are studied including the continuous dependence on initial conditions of the system's solution, the equilibrium stability, Hopf bifurcation at the equilibrium point, etc. This shows the rich dynamic behaviors of the system, including the supercritical Hopf bifurcations, subcritical Hopf bifurcations, and chaotic attractors. Numerical simulations are carried out to verify theoretical analyses and to exhibit the rich dynamic behaviors.

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Section: Modelmentioning

confidence: 99%

“…Let m = 1, R e and I e denote the real and imaginary parts of β 1 , then: 14 , the eigenvectors are obtained:…”

Section: Hopf Bifurcationmentioning

confidence: 99%

Dynamic Analysis of a Particle Motion System

Cui

2018

Mathematics

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Nonlinear dynamics of charged particle slipping on rough surface with periodic force

Ding

Zhang

2016

Nonlinear Dyn

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An investigation of the parameter space for a family of dissipative mappings

Oliveira

Montero

Costa

et al. 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The parameter plane investigation for a family of two-dimensional, nonlinear, and area contracting map is made. Several dynamical features in the system such as tangent, period-doubling, pitchfork, and cusp bifurcations were found and discussed together with cascades of period-adding, period-doubling, and the Feigeinbaum scenario. The presence of spring and saddle-area structures allow us to conclude that cubic homoclinic tangencies are present in the system. A set of complex sets such as streets with the same periodicity and the period-adding of spring-areas are observed in the parameter space of the mapping.

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A family of dissipative two-dimensional mappings: Chaotic, regular and steady state dynamics investigation

Cited by 5 publications

References 26 publications

Dynamic Analysis of a Particle Motion System

Dynamic Analysis of a Particle Motion System

Nonlinear dynamics of charged particle slipping on rough surface with periodic force

An investigation of the parameter space for a family of dissipative mappings

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