Driving-induced multistability in coupled chaotic oscillators: Symmetries and riddled basins

Ujjwal, Sangeeta Rani; Punetha, Nirmal; Ramaswamy, Ramakrishna; Agrawal, Manish; Prasad, Awadhesh

doi:10.1063/1.4954022

Cited by 25 publications

(18 citation statements)

References 34 publications

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“…8 where the boundary points seemed to span a two dimensional region in the two dimensional slice of the phase space. Our results also agree with previous studies of riddled basins of attraction where the uncertainty exponent α has been reported to be approximately zero 44 . Although the coupling strength chosen for Fig.…”

Section: Characteristics Of Basins Of Attractionsupporting

confidence: 93%

Riddled basins of attraction in systems exhibiting extreme events

Saha

Feudel

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Using a system of two FitzHugh-Nagumo units, we demonstrate the occurrence of riddled basins of attraction in delay-coupled systems as the coupling between the units is increased. We characterize riddled basins using the uncertainty exponent which is a measure of the dimensions of the basin boundary. Additionally, we show that the phase space can be partitioned into pure and mixed regions, where initial conditions in the pure regions certainly avoid the generation of extreme events, while initial conditions in the mixed region may or may not exhibit such events. This implies that any tiny perturbation of initial conditions in the mixed region could yield the emergence of extreme events because the latter state possesses a riddled basin of attraction.

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Section: Characteristics Of Basins Of Attractionsupporting

confidence: 93%

Riddled basins of attraction in systems exhibiting extreme events

Saha

Feudel

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…In the coupled system, the basin structure of the different attractors is complex [33]: there is a finite probability that two randomly selected nearby initial conditions will asymptote to different attractors (A ∓ and A 0 ). The measured uncertainty exponent lies close to zero, suggesting that the basins are effectively riddled (figure not shown here), but measures such as the transverse Lyapunov exponent and scaling laws [27] have not been straightforward to calculate.…”

Section: Basins Of Attractionmentioning

confidence: 99%

Emergence of chimeras through induced multistability

et al. 2017

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Chimeras, namely coexisting desynchronous and synchronized dynamics, are formed in an ensemble of identically coupled identical chaotic oscillators when the coupling induces multiple stable attractors, and further when the basins of the different attractors are intertwined in a complex manner. When there is coupling-induced multistability, an ensemble of identical chaotic oscillators-with global coupling, or also under the influence of common noise or an external drive (chaotic, periodic, or quasiperiodic)-inevitably exhibits chimeric behavior. Induced multistability in the system leads to the formation of distinct subpopulations, one or more of which support synchronized dynamics, while in others the motion is asynchronous or incoherent. We study the mechanism for the emergence of such chimeric states, and we discuss the generality of our results.

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“…At ε 1 = 0.023 the basin is completely interwoven in a complex manner and is completely intertwined for large volumes and it is very likely that the basin will be even more complicated for larger N . In general, the basin structure of different attractors in coupled systems is complex [26,27]. Thus there is finite probability that two randomly selected nearby initial conditions will asymptote to different regimes that may be synchronized or desynchronized.…”

Section: Basin Of Attraction and Lyapunov Exponentmentioning

confidence: 99%

Occurrence and stability of chimera states in multivariable coupled flows

Khatun,

Jafri

2019

Preprint

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Study of collective phenomenon in populations of coupled oscillators are a subject of intense exploration in physical, biological, neuronal and social systems. Here we propose a scheme for the creation of chimera states, namely the coexistence of distinct dynamical behaviors in an ensemble of multivariable coupled oscillatory systems and a novel scheme to study their stability. We target bifurcation parameters that can be tuned such that out of the two coupling parameters one pushes the system to synchrony while the other one takes it to the desynchronized state. The competition between these states result in a situation that a certain fraction of oscillators are synchronized while others are desynchronized thereby producing a mixed chimera state. Further changes in couplings can result in the desired form of the state which could be completely synchronized or desynchronized. Using the model example of coupled Rössler systems we show that their basin of attraction are either riddled or intertwined. We use Strength of incoherence and Master Stability function (MSF) as the order parameters to verify the stability of chimera states. MSF for different attractors are found to possess both negative and positive values indicating the coexistence of stable synchronized dynamics with desynchronized state.

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Driving-induced multistability in coupled chaotic oscillators: Symmetries and riddled basins

Cited by 25 publications

References 34 publications

Riddled basins of attraction in systems exhibiting extreme events

Riddled basins of attraction in systems exhibiting extreme events

Emergence of chimeras through induced multistability

Occurrence and stability of chimera states in multivariable coupled flows

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