Effect of repulsive links on frustration in attractively coupled networks (original) (raw)

Emergent multistability and frustration in phase-repulsive networks of oscillators

Physical Review E, 2011

The collective dynamics of oscillator networks with phase-repulsive coupling is studied, considering various network sizes and topologies. The notion of link frustration is introduced to characterize and quantify the network dynamical states. In opposition to widely studied phase-attractive case, the properties of final dynamical states in our model critically depend on the network topology. In particular, each network's total frustration value is intimately related to its topology. Moreover, phase-repulsive networks in general display multiple final frustration states, whose statistical and stability properties are uniquely identifying them.

Frustrations in Strongly Coupled Polygonal Oscillatory Networks

2014

Abstract—In this study, we investigate synchronization phenomena in two coupled polygonal oscillatory networks with strong frustrations. We focus on the amplitude of each oscillator when the coupling strength is increased. By using the computer simulations, we confirm that the amplitude of the oscillators decreases by increasing the coupling strength and oscillation death is occurred at un-frustrated oscillators.

Evolutionary design of non-frustrated networks of phase-repulsive oscillators

Scientific reports, 2012

Evolutionary optimisation algorithm is employed to design networks of phase-repulsive oscillators that achieve an anti-phase synchronised state. By introducing the link frustration, the evolutionary process is implemented by rewiring the links with probability proportional to their frustration, until the final network displaying a unique non-frustrated dynamical state is reached. Resulting networks are bipartite and with zero clustering. In addition, the designed non-frustrated anti-phase synchronised networks display a clear topological scale. This contrasts usually studied cases of networks with phase-attractive dynamics, whose performance towards full synchronisation is typically enhanced by the presence of a topological hierarchy.

Phase and amplitude dynamics of coupled oscillator systems on complex networks

Chaos, 2020

We investigated locking behaviors of coupled limit-cycle oscillators with phase and amplitude dynamics. We focused on how the dynamics are affected by inhomogeneous coupling strength and by angular and radial shifts in coupling functions. We performed mean-field analyses of oscillator systems with inhomogeneous coupling strength, testing Gaussian, power-law, and brain-like degree distributions. Even for oscillators with identical intrinsic frequencies and intrinsic amplitudes, we found that the coupling strength distribution and the coupling function generated a wide repertoire of phase and amplitude dynamics. These included fully and partially locked states in which high-degree or low-degree nodes would phase-lead the network. The mean-field analytical findings were confirmed via numerical simulations. The results suggest that, in oscillator systems in which individual nodes can independently vary their amplitude over time, qualitatively different dynamics can be produced via shift...

Synchronization of frustrated phase oscillators in the small-world networks

European Physical Journal Plus, 2022

We numerically study the synchronization of an identical population of Kuramoto-Sakaguchi phase oscillators in Watts-Strogatz networks. We find that, unlike random networks, phase-shift could enhance the synchronization in small-world networks. We also observe abrupt phase transition with hysteresis at some values of phase shifts in small-world networks, signs of an explosive phase transition. Moreover, we report the emergence of Chimera states at some values of phase-shift close to the transition points, which consist of spatially coexisting synchronized and desynchronized domains.

Perspective on attractive-repulsive interactions in dynamical networks: Progress and future

Europhysics Letters, 2020

Emerging collective behavior in complex dynamical networks depends on both coupling function and underlying coupling topology. Through this Perspective, we provide a brief yet profound excerpt of recent research efforts that explore how the synergy of attractive and repulsive interactions influence the destiny of ensembles of interacting dynamical systems. We review the incarnation of collective states ranging from chimera or solitary states to extreme events and oscillation quenching arising as a result of different network arrangements. Though the existing literature demonstrates that many of the crucial developments have been made, nonetheless, we come up with significant routes of further research in this field of study.

Contrariety and inhibition enhance synchronization in a small-world network of phase oscillators

2021

We numerically study the Kuramoto model's synchronization consisting of the two groups of conformistcontrarian and excitatory-inhibitory phase oscillators with equal intrinsic frequency. We consider random and small-world (SW) topologies for the connectivity network of the oscillators. In random networks, regardless of the contrarian to conformist connection strength ratio, we found a crossover from the π-state to the blurred πstate and then a continuous transition to the incoherent state by increasing the fraction of contrarians. However, for the excitatory-inhibitory model in a random network, we found that for all the values of the fraction of inhibitors, the two groups remain in-phase, and the transition point of fully synchronized to incoherent state reduced by strengthening the ratio of inhibitory to excitatory links. In the SW networks, we found that the order parameters for both models have not monotonic behavior in terms of the fraction of contrarians and inhibitors. Up to the optimal fraction of contrarians inhibitors, the synchronization rises by introducing the contrarians and inhibitors and then falls. We discuss that this non-monotonic behavior in synchronization is due to the weakening of the defects formed already in conformists and excitatory agents in SW networks.

Enhancing synchronization in complex networks of coupled phase oscillators

2007

By a model of coupled phase oscillators, we show analytically how synchronization in non-identical complex networks can be enhanced by introducing a proper gradient into the couplings. It is found that, by pointing the gradient from the large-degree to the small-degree nodes on each link, increase of the gradient strength will bring forward the onset of network synchronization monotonically, and, with the same gradient strength, heterogeneous networks are more synchronizable than homogeneous networks. The findings are tested by extensive simulations and good agreement are found.

Synchronization in large directed networks of coupled phase oscillators

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2006

We extend recent theoretical approximations describing the transition to synchronization in large undirected networks of coupled phase oscillators to the case of directed networks. We also consider extensions to networks with mixed positive/negative coupling strengths. We compare our theory with numerical simulations and find good agreement.

Explosive transitions to synchronization in networks of phase oscillators

Scientific Reports, 2013

The emergence of dynamical abrupt transitions in the macroscopic state of a system is currently a subject of the utmost interest. The occurrence of a first-order phase transition to synchronization of an ensemble of networked phase oscillators was reported, so far, for very particular network architectures. Here, we show how a sharp, discontinuous transition can occur, instead, as a generic feature of networks of phase oscillators. Precisely, we set conditions for the transition from unsynchronized to synchronized states to be first-order, and demonstrate how these conditions can be attained in a very wide spectrum of situations. We then show how the occurrence of such transitions is always accompanied by the spontaneous setting of frequency-degree correlation features. Third, we show that the conditions for abrupt transitions can be even softened in several cases. Finally, we discuss, as a possible application, the use of this phenomenon to express magnetic-like states of synchronization. M any complex systems operate transitions between different regimes or phases under the action of a control parameter. These transitions can be monitored using a global order parameter, a physical quantity (e.g. scalar, vector, …) accounting for the symmetry of the phases. Phase transitions can be of first or second order according to whether the order parameter varies continuously or discontinuously at a critical value of the control parameter. In complex networks theory 1 , phase transitions have been observed in the way the graph collectively organizes its architecture (e.g. percolation 2,3 ) and dynamical state (e.g. synchronization 4-6 ).