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

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 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.

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.

Phase clustering in complex networks of delay-coupled oscillators

2011

We study the clusterization of phase oscillators coupled with delay in complex networks. For the case of difussive oscillators, we formulate the equations relating the topology of the network and the phases and frequencies of the oscillators (functional response). We solve them exactly in directed networks for the case of perfect synchronization. We also compare the reliability of the solution of the linear system for non-linear couplings. Taking advantage of the form of the solution, we propose a frequency adaptation rule to achieve perfect synchronization. We also propose a mean-field theory for uncorrelated random networks that proves to be pretty accurate to predict phase synchronization in real topologies, as for example the C.elegans or the Autonomous Systems connectivity. *

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 ).

Effective Subnetwork Topology for Synchronizing Interconnected Networks of Coupled Phase Oscillators

Frontiers in computational neuroscience, 2018

A system consisting of interconnected networks, or a network of networks (NoN), appears diversely in many real-world systems, including the brain. In this study, we consider NoNs consisting of heterogeneous phase oscillators and investigate how the topology of subnetworks affects the global synchrony of the network. The degree of synchrony and the effect of subnetwork topology are evaluated based on the Kuramoto order parameter and the minimum coupling strength necessary for the order parameter to exceed a threshold value, respectively. In contrast to an isolated network in which random connectivity is favorable for achieving synchrony, NoNs synchronize with weaker interconnections when the degree distribution of subnetworks is heterogeneous, suggesting the major role of the high-degree nodes. We also investigate a case in which subnetworks with different average natural frequencies are coupled to show that direct coupling of subnetworks with the largest variation is effective for s...

Entraining the topology and the dynamics of a network of phase oscillators

Physical Review E, 2009

We show that the topology and dynamics of a network of unsynchronized Kuramoto oscillators can be simultaneously controlled by means of a forcing mechanism which yields a phase locking of the oscillators to that of an external pacemaker in connection with the reshaping of the network's degree distribution. The entrainment mechanism is based on the addition, at regular time intervals, of unidirectional links from oscillators that follow the dynamics of a pacemaker to oscillators in the pristine graph whose phases hold a prescribed phase relationship. Such a dynamically based rule in the attachment process leads to the emergence of a power-law shape in the final degree distribution of the graph whenever the network is entrained to the dynamics of the pacemaker. We show that the arousal of a scale-free distribution in connection with the success of the entrainment process is a robust feature, characterizing different networks' initial configurations and parameters.

Synchronization in complex networks of phase oscillators: A survey

Automatica, 2014

The emergence of synchronization in a network of coupled oscillators is a fascinating subject of multidisciplinary research. This survey reviews the vast literature on the theory and the applications of complex oscillator networks. We focus on phase oscillator models that are widespread in real-world synchronization phenomena, that generalize the celebrated Kuramoto model, and that feature a rich phenomenology. We review the history and the countless applications of this model throughout science and engineering. We justify the importance of the widespread coupled oscillator model as a locally canonical model and describe some selected applications relevant to control scientists, including vehicle coordination, electric power networks, and clock synchronization. We introduce the reader to several synchronization notions and performance estimates. We propose analysis approaches to phase and frequency synchronization, phase balancing, pattern formation, and partial synchronization. We present the sharpest known results about synchronization in networks of homogeneous and heterogeneous oscillators, with complete or sparse interconnection topologies, and in finite-dimensional and infinite-dimensional settings. We conclude by summarizing the limitations of existing analysis methods and by highlighting some directions for future research.

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.