Aging transition by random errors

Sun, Zhongkui; Ma, Ning; Xu, Wei

doi:10.1038/srep42715

Cited by 30 publications

(12 citation statements)

References 29 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.…”

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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“…Further, it has been identified that the addition of asymmetry or feedback parameter enhances the dynamical robustness in an aging network [38,39]. Effects of time-delay or random errors on the aging behavior have also been studied by varying the proportion of inactive oscillators [40,41]. Very recently, the aging transition in weighted homogeneous and heterogeneous networks has also been reported [42].…”

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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“…Addition of supporting oscillators to damaged networks can develop the survivability of the networks [71]. Random errors in the parameters of the local dynamical units can also bring global rhythmicity back [72]. Recently, the authors of [73] studied that a global feedback from all the nodes helps in augmenting dynamical persistence.…”

Section: Introductionmentioning

confidence: 99%

Dynamical robustness of complex networks subject to long-range connectivity

Majhi

2022

Proc. R. Soc. A.

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In spite of a few attempts in understanding the dynamical robustness of complex networks, this extremely important subject of research is still in its dawn as compared to the other dynamical processes on networks. We hereby consider the concept of long-range interactions among the dynamical units of complex networks and demonstrate for the first time that such a characteristic can have noteworthy impacts on the dynamical robustness of networked systems, regardless of the underlying network topology. We present a comprehensive analysis of this phenomenon on top of diverse network architectures. Such dynamical damages being able to substantially affect the network performance, determining mechanisms that boost the robustness of networks becomes a fundamental question. In this work, we put forward a prescription based upon self-feedback that can efficiently resurrect global rhythmicity of complex networks composed of active and inactive dynamical units, and thus can enhance the network robustness. We have been able to delineate the whole proposition analytically while dealing with all d -path adjacency matrices, having an excellent agreement with the numerical results. For the numerical computations, we examine scale-free networks, Watts–Strogatz small-world model and also Erdös–Rényi random network, along with Landau–Stuart oscillators for casting the local dynamics.

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Aging transition by random errors

Cited by 30 publications

References 29 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

Dynamical robustness of complex networks subject to long-range connectivity

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