Transition from amplitude to oscillation death under mean-field diffusive coupling

Banerjee, Tanmoy; Ghosh, Debarati

doi:10.1103/physreve.89.052912

Cited by 82 publications

(21 citation statements)

References 32 publications

(42 reference statements)

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“…Earlier investigations on the phenomenon of chimera were restricted to nonlocal coupling, both in the weak and the strong coupling limits, giving rise to frequency [19,20] and amplitude chimeras [21,22,20,23,24,27,28], as it was believed that nonlocal coupling is a prerequisite for the onset of chimera in an ensemble of identical oscillators. Later investigations revealed the emergence of chimera states under global coupling [29,30,31,32], mean-field coupling [44] and even in nearest neighbor coupling [45,46]. In addition to the frequency and amplitude chimeras, other types of chimera states such as amplitude mediated chimeras [47], intensity induced chimeras [48], and chimera death [22,32,40,49,50] were also reported in the recent literature.…”

Section: Introductionmentioning

confidence: 88%

Chimera at the phase-flip transition of an ensemble of identical nonlinear oscillators

Gopal¹,

Chandrasekar²,

Senthilkumar³

et al. 2018

Communications in Nonlinear Science and Numerical Simulation

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A complex collective emerging behavior characterized by coexisting coherent and incoherent domains is termed as a chimera state. We bring out the existence of a new type of chimera in a nonlocally coupled ensemble of identical oscillators driven by a common dynamic environment. The latter facilitates the onset of phase-flip bifurcation/transitions among the coupled oscillators of the ensemble, while the nonlocal coupling induces a partial asynchronization among the out-of-phase synchronized oscillators at this onset. This leads to the manifestation of coexisting out-of-phase synchronized coherent domains interspersed by asynchronous incoherent domains elucidating the existence of a different type of chimera state. In addition to this, a rich variety of other collective behaviors such as clusters with phase-flip transition, conventional chimera, solitary state and complete synchronized state which have been reported using different coupling architectures are found to be induced by the employed couplings for appropriate coupling strengths. The robustness of the resulting dynamics is demonstrated in ensembles of two paradigmatic models, namely Rössler oscillators and Stuart-Landau oscillators.

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Section: Introductionmentioning

confidence: 88%

Chimera at the phase-flip transition of an ensemble of identical nonlinear oscillators

Gopal¹,

Chandrasekar²,

Senthilkumar³

et al. 2018

Communications in Nonlinear Science and Numerical Simulation

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show abstract

“…The observation is shown in Fig.3. Note that in Fig.3 in AD region ' is non zero which is the characteristic of a nontrivial AD, thus OD and possibly a nontrivial AD coexists as discovered in [14], [15]. It is also observed that the difference between two IHSS for ' state variable gradually increases as we increase the + value but remain unaltered for variation of and values.…”

Section: Numerical Simulation Resultsmentioning

confidence: 64%

“…After then several works have been reported showing such transition in different coupled system like; mean field diffusive (MFD) coupled system [14], [15], time-delayed system [16], dynamic coupled system [17], conjugate coupled system [18], [19], diffusive and repulsive coupled system [20], [21] etc.…”

Section: Introductionmentioning

confidence: 99%

Untitled

2018

IJET

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“…In an assembly of coupled systems, amplitude death emerges mainly due to specific nature of coupling like transmission delay, processing delay, dynamic coupling, nonlinear coupling, environmental coupling, etc. or due to parameter mismatch 33,34,[36][37][38][39][40][41][42][43] or time scale diversity 44,45 . Most often, amplitude death is required to suppress unwanted oscillations in connected systems.…”

Section: Introductionmentioning

confidence: 99%

Role of time scales and topology on the dynamics of complex networks

Gupta

Ambika

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The interplay between time scales and structural properties of complex networks of nonlinear oscillators can generate many interesting phenomena, like amplitude death, cluster synchronization, frequency synchronization etc. We study the emergence of such phenomena and their transitions by considering a complex network of dynamical systems in which a fraction of systems evolves on a slower time scale on the network. We report the transition to amplitude death for the whole network and the scaling near the transitions as the connectivity pattern changes. We also discuss the suppression and recovery of oscillations and the cross over behavior as the number of slow systems increases. By considering a scale free network of systems with multiple time scales, we study the role of heterogeneity in link structure on dynamical properties and the consequent critical behaviors. In this case with hubs made slow, our main results are the escape time statistics for loss of complete synchrony as the slowness spreads on the network and the self-organization of the whole network to a new frequency synchronized state. Our results have potential applications in biological, physical, and engineering networks consisting of heterogeneous oscillators.Complexity of real world systems are studied mainly in terms of the nonlinearity in the intrinsic dynamics of their sub systems and the complex interaction patterns among them. In such systems, the variability and heterogeneity of the interacting sub systems can add a further level of complexity. In this context heterogeneity arising from differing dynamical time scales offers several challenges and has applications in diverse fields, ranging from biology, economy, sociology to physics and engineering. In our work, we study the interesting cooperative dynamics in interacting nonlinear systems of differing time scales using the frame work of complex networks.

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Transition from amplitude to oscillation death under mean-field diffusive coupling

Cited by 82 publications

References 32 publications

Chimera at the phase-flip transition of an ensemble of identical nonlinear oscillators

Chimera at the phase-flip transition of an ensemble of identical nonlinear oscillators

Untitled

Role of time scales and topology on the dynamics of complex networks

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