Aging transition in the absence of inactive oscillators

Sathiyadevi, K.; Gowthaman, I.; Senthilkumar, D. V.; Chandrasekar, V. K.

doi:10.1063/1.5121565

Cited by 15 publications

(6 citation statements)

References 65 publications

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“…In an effort to understand the origin of this transition-which does not appear to be the consequence of a simple majority rule-a number of variations of the initial model [1] have been studied, by incorporating distributed time delays [4,5], by varying the network topology [6,7], or by introducing heterogeneity in the parameters [8,9] as well as by including noise [10]. The nature of the coupling between the oscillators-whether through similar or dissimilar variables [11,12]-has also been explored in some detail over the past few years. One conclusion that can be drawn from this large variety of studies is that the essential feature that is required in an ensemble that exhibits the transition to stasis or ageing is heterogeneity or diversity in the components or in the interactions: some form of dynamical frustration seems necessary.…”

Section: Introductionmentioning

confidence: 99%

Stasis in heterogeneous networks of coupled oscillators: discontinuous transition with hysteresis

2023

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We consider a heterogenous ensemble of dynamical systems in $\mathbb{R}^4$ that individually are either attracted to fixed points (and are termed inactive) or to limit cycles (in which case they are termed active). These distinct states are separated by bifurcations that are controlled by a single parameter. Upon coupling them globally, we find a {\em discontinuous} transition to global inactivity (or {\em stasis}) when the proportion of inactive components in the ensemble exceeds a threshold: there is a first--order phase transition from a globally oscillatory state to global oscillation death. There is hysteresis associated with these phase transitions. Numerical results for a representative system are supported by analysis using a system-reduction technique and different dynamical regimes can be rationalised through the corresponding bifurcation diagrams of the reduced set of equations. 

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Section: Introductionmentioning

confidence: 99%

Stasis in heterogeneous networks of coupled oscillators: discontinuous transition with hysteresis

2023

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“…On the other hand, deterioration or degrading of dynamical activity is also a severe issue which exists in many complex networks, for instance, cascading failure of power grids, and decreasing efficiency of living organisms are a few examples of such degradations [22,34,35]. Originally, this was reported by Daido et al in globally coupled oscillators [36].…”

Section: Introductionmentioning

confidence: 99%

Aging transition under discrete time-dependent coupling: Restoring rhythmicity from aging

Sathiyadevi,

Premraj,

Banerjee

et al. 2022

Preprint

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We explore the aging transition in a network of globally coupled Stuart-Landau oscillators under a discrete time-dependent coupling. In this coupling, the connections among the oscillators are turned ON and OFF in a systematic manner, having either a symmetric or an asymmetric time interval. We discover that depending upon the time period and duty cycle of the ON-OFF intervals, the aging region shrinks drastically in the parameter space, therefore promoting restoration of oscillatory dynamics from the aging. In the case of symmetric discrete coupling (where the ON-OFF intervals are equal), the aging zone decreases significantly with the resumption of dynamism with an increasing time period of the ON-OFF intervals. On the other hand, in the case of asymmetric coupling (where the ON-OFF intervals are not equal), we find that the ratio of the ON and OFF intervals controls the aging dynamics: the aging state is revoked more effectively if the interval of the OFF state is greater than the ON state. Finally, we study the transition in aging using a discrete pulse coupling: we note that the pulse interval plays a crucial role in determining the aging region. For all the cases of discrete time-dependent couplings, the aging regions are shrinking and the

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“…Further, the breaking of rotational symmetry induced dynamical effects were investigated in counter-rotating oscillators with symmetry preserving and symmetry breaking couplings [44]. Recently, the aging transitions have also been investigated in counterrotating oscillators [45]. Therefore, competing co-and counter-rotating frequencies play an essential role in exhibiting a distinct set of collective behaviors including mixed synchronization and different oscillation quenching states.…”

Section: Introductionmentioning

confidence: 99%

Emerging chimera states under non-identical counter-rotating oscillators

Sathiyadevi,

Chandrasekar,

Lakshmanan

2022

Preprint

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Frequency plays a crucial role in exhibiting various collective dynamics in the coexisting co-and counter-rotating systems. To illustrate the impact of counter-rotating frequencies, we consider a network of non-identical and globally coupled Stuart-Landau oscillators with additional perturbation. Primarily, we investigate the dynamical transitions in the absence of perturbation, demonstrating that the transition from desynchronized state to cluster oscillatory state occurs through an interesting partial synchronization state in the oscillatory regime. Followed by this, the system dynamics transits to amplitude death and oscillation death states. Importantly, we find that the observed dynamical states do not preserve the parity(P ) symmetry in the absence of perturbation. When the perturbation is increased one can note that the system dynamics exhibits a new kind of transition which corresponds to a change from incoherent mixed synchronization to coherent mixed synchronization through chimera state. In particular, incoherent mixed synchronization and coherent mixed synchronization states completely preserve the P -symmetry, whereas the chimera state preserves the P -symmetry only partially. To demonstrate the occurrence of such partial symmetry breaking (chimera) state, we use basin stability analysis and discover that partial symmetry breaking exists as a result of the coexistence of symmetry preserving and symmetry breaking behavior in the initial state space. Further, a measure of the strength of P -symmetry is established to quantify the P -symmetry in the observed dynamical states. Subsequently, the dynamical transitions are investigated in the parametric spaces. Finally, by increasing the network size, the robustness of the chimera state is also inspected and we find that the chimera state is robust even in networks of larger sizes. We also show the generality of the above results in the related phase reduced model as well as in other coupled models such as the globally coupled van der Pol and Rössler oscillators.

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Aging transition in the absence of inactive oscillators

Cited by 15 publications

References 65 publications

Stasis in heterogeneous networks of coupled oscillators: discontinuous transition with hysteresis

Stasis in heterogeneous networks of coupled oscillators: discontinuous transition with hysteresis

Aging transition under discrete time-dependent coupling: Restoring rhythmicity from aging

Emerging chimera states under non-identical counter-rotating oscillators

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