Robustness of coupled oscillator networks with heterogeneous natural frequencies

Abstract

Robustness of coupled oscillator networks against local degradation of oscillators has been intensively studied in this decade. The oscillation behavior on the whole network is typically reduced with an increase in the fraction of degraded (inactive) oscillators. The critical fraction of inactive oscillators, at which a transition from an oscillatory to a quiescent state occurs, has been used as a measure for the network robustness. The larger (smaller) this measure is, the more robust (fragile) the oscillatory behavior on the network is. Most previous studies have used oscillators with identical natural frequencies, for which the oscillators are necessarily synchronized and thereby the analysis is simple. In contrast, we focus on the effect of heterogeneity in the natural frequencies on the network robustness. First, we analytically derive the robustness measure for the coupled oscillator models with heterogeneous natural frequencies under some conditions. Then, we show that increasing the heterogeneity in natural frequencies makes the network fragile. Moreover, we discuss the optimal parameter condition to maximize the network robustness.

Augmentation of dynamical persistence in networks through asymmetric interaction

“…This sort of complete deterioration in networks as a function of the fraction of malfunctioned (a) E-mail: biswambhar.rakshit@gmail.com units was then named as aging transition. But this study of dynamical robustness [9][10][11][12][13][14][15][16][17][18][19][20] of networks is different from its structural counterpart [21][22][23][24][25] which mainly deals with network resilience against structural perturbations in terms of node removal or link failure.…”

“…eq. ( 4)), we plot its dependence on the simultaneous variation of the coupling strength ∈ [10, 100] and asymmetry parameter m ∈ [1,10] for a small-world network in fig. 6(b).…”

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

“…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.…”