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Physics Reports 660, 1-94,. Almendral, +5 authors Y. transition explosive transitions in complex networks’ structure and dynamics: percolation and synchronization is disclosed by the behavior of the order parameter at criticality. Rodrigues et al-Effects of degree correlations on the explosive synchronization of scale-free networks I.

· Explosive percolation, which was discovered in, corresponds to an abrupt change in the network’s structure, and explosive synchronization (which is concerned, instead, with the abrupt emergence of a collective state in the networks’ dynamics) was studied as early as the first models of globally coupled phase oscillators were taken into consideration. Explosive collective phenomena have attracted much attention since the discovery explosive transitions in complex networks’ structure and dynamics: percolation and synchronization explosive transitions in complex networks’ structure and dynamics: percolation and synchronization of an explosive percolation transition. The results of our study indicate that the mesoscopic structure of the networks could affect the synchron.

Boccaletti et al-The Kuramoto model in complex networks Francisco A. Journal of Statistical Mechanics: Theory and Experiment :8, 083404. () Dynamic mechanical properties explosive transitions in complex networks’ structure and dynamics: percolation and synchronization and mesostructure evolution of granular materials subjected to cyclic loading. Nonstandard explosive transitions in complex networks’ structure and dynamics: percolation and synchronization transitions in the Kuramoto model: a role of asymmetry in natural frequency distributions Yu Terada, Keigo Ito, Toshio Aoyagi et al. Based on Kuramoto oscillators, ES has rapidly become a subject of enormous interest 22,23,24,25,26,27,28,29,30,31,32. complex networks’ structure and dynamics. This indicates that coherence alone cannot be enough to explain all the. Models of explosive synchronization provide an analytic framework for the dynamics of abrupt transitions and reveal the interplay between the distribution in natural frequencies and the network structure, with explosive transitions in complex networks’ structure and dynamics: percolation and synchronization applications ranging from epileptic seizures to waking from anesthesia.

· It is an interdiscipline of statistical physics and nonlinear science, because these non-equilibrium systems may exhibit phase transitions. Explosive percolation, which was discovered in, corresponds to an abrupt explosive transitions in complex networks’ structure and dynamics: percolation and synchronization change in the network&39;s structure, and explosive synchronization (which is concerned, instead, with the abrupt. Explosive transitions in complex networks’ structure and dynamics: Percolation and synchronization S Boccaletti, JA Almendral, S Guan, I Leyva, Z Liu, I Sendiña-Nadal,.

She is the author of the book Multilayer Networks: Structure and Function by Oxford University Press. · Recently, however, explosive phenomena have been reported in com- plex networks&39; structure and dynamics, which explosive transitions in complex networks’ structure and dynamics: percolation and synchronization rather remind first-order (discontinuous and irreversible) transitions. In complex networks theory1, phase transitions have been observed in the way the graph collectively organizes its architecture (e. The adaptive mechanisms here considered not only enhance synchronization and percolation, but also make () (), (() ().

Abstract and Figures It has been recently reported that explosive synchronization transitions can take place in dynamics: networks of phase oscillators Gómez-Gardeñes et al. Explosive percolation, which was discovered in, corresponds to an abrupt change in the network&39;s structure, and explosive synchronization (which is concerned, instead, with the abrupt emergence of a collective state in the networks&39; dynamics) was studied as early as the first explosive transitions in complex networks’ structure and dynamics: percolation and synchronization models of globally coupled phase oscillators explosive transitions in complex networks’ structure and dynamics: percolation and synchronization were taken into consideration. · Explosive percolation, which was discovered in, corresponds to an abrupt change in the network&39;s structure, and explosive synchronization (which is concerned, instead, with the abrupt emergence of a collective state in explosive transitions in complex networks’ structure and dynamics: percolation and synchronization the networks&39; dynamics) was studied as early as the first models of globally coupled phase oscillators were taken into consideration. Then, the synchronization dynamics explosive transitions in complex networks’ structure and dynamics: percolation and synchronization is studied of a network of identical Rössler explosive transitions in complex networks’ structure and dynamics: percolation and synchronization oscillators under variation of the network degree correlation properties. The precursory microtransitions allow us to target almost deterministically the location of the transition point to global connectivity.

Onset and loss of synchronization in coupled oscillators are of fundamental importance in understanding emergent behavior in natural and man-made systems, which range from neural networks to power grids. by a discontinuous transition, called explosive synchronization (ES) 21. At present, many results of ES are based on the networked Kuramoto oscillators and little attention has been paid to the influence of chaotic dynamics on synchronization transitions. Thus, there is great interest in analyzing phase transitions to large-scale connectivity and to global synchronization, including how to enhance or delay the onset.

percolation 2,3 ) and dynamical state (e. percolation2,3) and dynamical state (e. Even when increasing the level of synchronization in a biological system is considered dynamics: as the main driving force for adaptation, there is evidence of explosive transitions in complex networks’ structure and dynamics: percolation and synchronization negative effects induced by excessive synchronization. These phenomena are traditionally studied as second-order phase transitions.

Explosive explosive transitions in complex networks’ structure and dynamics: percolation and synchronization transitions in complex networks structure and dynamics: Percolation and synchronization explosive transitions in complex networks’ structure and dynamics: percolation and synchronization S. In complex networks’ theory 1,2 such phase transitions have been observed in the way a graph collectively organizes its architecture through percolation 3–5, and its dynamical state through synchronization, both for continuous 6,7 and discrete 8 dynamical. Explosive percolation, discovered in, corresponds to an abrupt change in the network’s structure, and dynamics: explosive synchronization generates a sudden emergence explosive transitions in complex networks’ structure and dynamics: percolation and synchronization of a collective state in the networks’ dynamics. Physics Reports explosive transitions in complex networks’ structure and dynamics: percolation and synchronization 660, 1-94, explosive transitions in complex networks’ structure and dynamics: percolation and synchronization In this paper, explosive transitions in complex networks’ structure and dynamics: percolation and synchronization we analyze explosive synchronization in networks with a community structure. In the last years, she has been focusing on multilayer networks, simplicial complexes, network geometry explosive transitions in complex networks’ structure and dynamics: percolation and synchronization and topology, explosive transitions in complex networks’ structure and dynamics: percolation and synchronization percolation and network control. Explosive synchronization and explosive percolation are currently two independent phenomena occurring in complex networks, where the former takes place in dynamical phase space while the latter in configuration space.

In the current work, our aim is to study the synchronization dynamics of coupled oscillators on complex networks. Google Scholar 15. For some systems satisfying explosive transitions in complex networks’ structure and dynamics: percolation and synchronization certain symmetries, the dynamics of high-dimensional space can be reduced to that of low-dimensional subspace in terms of the Watanabe–Strogatz theory. We report the discovery of a discrete hierarchy of microtransitions occurring in models of continuous and discontinuous percolation. More recently, the emergence of explosive synchronization of coupled phase oscillators has attracted much attention due to the discovery of an explosive percolation transition in complex networks 613. · We evaluate the efficiency of our methods using various paradigmatic network models and apply the novel concepts to identify important edges and important sets of edges in a commonly used benchmark model in social network analysis, as well as in evolving epileptic brain networks.

Sendiña-Nadal et al-This content was downloaded from IP address 207. Together with the great progress in EP, it has been argued that also synchronization transitions on SF networks can occur explosive transitions in complex networks’ structure and dynamics: percolation and synchronization explosively, i. Rodrigues et al-. Explosive synchronization (ES), as one kind of abrupt dynamical transitions in nonlinearly coupled systems, has become a hot spot of modern complex networks. This extends to the class of intrinsically stochastic processes the possibility to use warning signals anticipating phase.

Explosive percolation, which was discovered explosive transitions in complex networks’ structure and dynamics: percolation and synchronization in, corresponds to an abrupt change in the network&39;s structure, and explosive explosive transitions in complex networks’ structure and dynamics: percolation and synchronization synchronization (which is concerned. network’s structure and dynamics, thence supporting the ubiquity explosive transitions in complex networks’ structure and dynamics: percolation and synchronization of synchronized and connected components in complex systems under limited resources for interactions. Explosive synchronization, an abrupt transition to a collective coherent state, has been the focus of an extensive research since its first explosive transitions in complex networks’ structure and dynamics: percolation and synchronization observation in scale-free networks with degree-frequency correlations. Explosive transitions in complex networks’ structure and dynamics: Percolation and synchronization S. () Explosive synchronization induced by traffic processes in explosive transitions in complex networks’ structure and dynamics: percolation and synchronization complex networks.

· Collective behaviors of coupled oscillators are an important issue in the field of nonlinear dynamics and complex networks, which have attracted much attention in recent years. · She has worked in network entropy and network ensembles and on dynamical processes on networks. In this paper, the dynamics of the. synchronization 4–6 ). · Adaptation plays a fundamental role in shaping the structure of a complex network and improving its functional fitting.

We report on experiments with hundreds of strongly coupled photochemical relaxation oscillators that exhibit a discontinuous synchronization transition with hysteresis, as opposed explosive transitions in complex networks’ structure and dynamics: percolation and synchronization to the. In this Letter, we demonstrate how an explosive transition shows up in the synchronization of complex heterogeneous networks by incorporating a microscopic correlation between the structural and the dynamical properties of the system. transitions phenomena have been reported in complex networks’ structure and dynamics. In this Letter, we demonstrate how an explosive transition shows up in the synchronization of scale-free networks by incorporating a microscopic correlation between the structural and the dynamical properties of the system. of an explosive percolation transition in complex networks. Recently, however, explosive phenomena have been reported in com- plex networks&39; structure and dynamics, which rather remind first-order (discontinuous and irreversible) transitions. The emergence of large-scale connectivity and synchronization are crucial to the structure, function and failure of many complex socio-technical networks.

-Recent citations Explosive transitions in complex networks structure and dynamics: Percolation and synchronization S. Zhao, Global synchronization of complex dynamical networks with non-identical nodes, in 47th IEEE Conference on Decision and Control, IEEE,,817–822. The two phenomena have stimulated. · Explosive transitions in complex networks’ structure and dynamics: Percolation and synchronization. Therefore, the first task is to build a substrate network, which follows the steps below 11 12. The characteristics of this ex-. We observe that negative correlation has a positive effect on the synchronization dynamics of such networks.

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