Robust attractor of non-twist systems

Carvalho, R. Egydio de; Abud, C. Vieira

doi:10.1016/j.physa.2015.08.008

Cited by 7 publications

(1 citation statement)

References 28 publications

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“…4 (B) and Both questions can be evaluated by calculating the Lyapunov exponents onto the space of the parameters. Such Lyapunov exponents are standard measures used to discriminate between chaos and periodicity and, the projection of Lyapunov exponents onto the space of the parameters is called Lyapunov diagrams [17][18][19] .…”

Section: Numerical Analysismentioning

confidence: 99%

Nonlinear Behavior of a Suspended Particle in Single-Axis Acoustic Levitators

Abud

Rodrigues

Ramos

2019

Int J Innov Educ Res

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The nonlinear behavior of a suspended sphere in a single-axis acoustic levitator was studied. Spontaneous oscillations of the sphere in this levitator were experimentally analyzed recording its positions using a high speed camera. A mathematical model based on acoustic radiation forces and real parameters is proposed to describe the dynamics of the sphere movement and its stability. The stability of the motion was investigated via a Lyapunov exponent diagram. We observed that the axial and radial movements of small spheres under levitation may present regular stability and chaotic ones. The Lyapunov exponent diagram for the model shows a complexity structure sharing different regions of stability according to the model parameters.

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Section: Numerical Analysismentioning

confidence: 99%

Nonlinear Behavior of a Suspended Particle in Single-Axis Acoustic Levitators

Abud

Rodrigues

Ramos

2019

Int J Innov Educ Res

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Manifestation of Multistability in Different Systems

Pisarchik

Hramov

2022

Multistability in Physical and Living Systems

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Curry–Yorke route to shearless attractors and coexistence of attractors in dissipative nontwist systems

Mugnaine

Batista

Caldas

et al. 2021

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The routes to chaos play an important role in predictions about the transitions from regular to irregular behavior in nonlinear dynamical systems, such as electrical oscillators, chemical reactions, biomedical rhythms, and nonlinear wave coupling. Of special interest are dissipative systems obtained by adding a dissipation term in a given Hamiltonian system. If the latter satisfies the so-called twist property, the corresponding dissipative version can be called a “dissipative twist system.” Transitions to chaos in these systems are well established; for instance, the Curry–Yorke route describes the transition from a quasiperiodic attractor on torus to chaos passing by a chaotic banded attractor. In this paper, we study the transitions from an attractor on torus to chaotic motion in dissipative nontwist systems. We choose the dissipative standard nontwist map, which is a non-conservative version of the standard nontwist map. In our simulations, we observe the same transition to chaos that happens in twist systems, known as a soft one, where the quasiperiodic attractor becomes wrinkled and then chaotic through the Curry–Yorke route. By the Lyapunov exponent, we study the nature of the orbits for a different set of parameters, and we observe that quasiperiodic motion and periodic and chaotic behavior are possible in the system. We observe that they can coexist in the phase space, implying in multistability. The different coexistence scenarios were studied by the basin entropy and by the boundary basin entropy.

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Robust attractor of non-twist systems

Cited by 7 publications

References 28 publications

Nonlinear Behavior of a Suspended Particle in Single-Axis Acoustic Levitators

Nonlinear Behavior of a Suspended Particle in Single-Axis Acoustic Levitators

Manifestation of Multistability in Different Systems

Curry–Yorke route to shearless attractors and coexistence of attractors in dissipative nontwist systems

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