Collective dynamics of random Janus oscillator networks
04 Mar 2020-Vol. 2, Iss: 1, pp 013255
TL;DR: In this article, the authors show that for random networks of Janus oscillators there is coexistence of partial synchronization and a novel form of collective state denominated breathing standing waves, along with abrupt synchronization transitions.
Abstract: This paper shows that for random networks of Janus oscillators there is coexistence of partial synchronization and a novel form of collective state denominated breathing standing waves, along with abrupt synchronization transitions.
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TL;DR: DART generalizes recent approaches for dimension reduction by allowing the treatment of complex-valued dynamical variables, heterogeneities in the intrinsic properties of the nodes as well as modular networks with strongly interacting communities.
Abstract: Several complex systems can be modeled as large networks in which the state of the nodes continuously evolves through interactions among neighboring nodes, forming a high-dimensional nonlinear dynamical system. One of the main challenges of Network Science consists in predicting the impact of network topology and dynamics on the evolution of the states and, especially, on the emergence of collective phenomena, such as synchronization. We address this problem by proposing a Dynamics Approximate Reduction Technique (DART) that maps high-dimensional (complete) dynamics unto low-dimensional (reduced) dynamics while preserving the most salient features, both topological and dynamical, of the original system. DART generalizes recent approaches for dimension reduction by allowing the treatment of complex-valued dynamical variables, heterogeneities in the intrinsic properties of the nodes as well as modular networks with strongly interacting communities. Most importantly, we identify three major reduction procedures whose relative accuracy depends on whether the evolution of the states is mainly determined by the intrinsic dynamics, the degree sequence, or the adjacency matrix. We use phase synchronization of oscillator networks as a benchmark for our threefold method. We successfully predict the synchronization curves for three phase dynamics (Winfree, Kuramoto, theta) on the stochastic block model. Moreover, we obtain the bifurcations of the Kuramoto-Sakaguchi model on the mean stochastic block model with asymmetric blocks and we show numerically the existence of periphery chimera state on the two-star graph. This allows us to highlight the critical role played by the asymmetry of community sizes on the existence of chimera states. Finally, we systematically recover well-known analytical results on explosive synchronization by using DART for the Kuramoto-Sakaguchi model on the star graph.
12 citations
11 Nov 2020
TL;DR: In this article, a dynamics approximate reduction technique is introduced to provide low-dimensional representations of dynamics on complex networks, and use it to predict synchronization phenomena emerging from oscillator dynamics.
Abstract: This paper introduces a dynamics approximate reduction technique to provide low-dimensional representations of dynamics on complex networks, and use it to predict synchronization phenomena emerging from oscillator dynamics.
11 citations
TL;DR: It is shown that uncorrelated noise can in fact enhance synchronization when the oscillators are coupled, and that the same effect can be harnessed in engineered systems.
Abstract: Synchronization is a widespread phenomenon observed in physical, biological, and social networks, which persists even under the influence of strong noise. Previous research on oscillators subject to common noise has shown that noise can actually facilitate synchronization, as correlations in the dynamics can be inherited from the noise itself. However, in many spatially distributed networks, such as the mammalian circadian system, the noise that different oscillators experience can be effectively uncorrelated. Here, we show that uncorrelated noise can in fact enhance synchronization when the oscillators are coupled. Strikingly, our analysis also shows that uncorrelated noise can be more effective than common noise in enhancing synchronization. We first establish these results theoretically for phase and phase-amplitude oscillators subject to either or both additive and multiplicative noise. We then confirm the predictions through experiments on coupled electrochemical oscillators. Our findings suggest that uncorrelated noise can promote rather than inhibit coherence in natural systems and that the same effect can be harnessed in engineered systems.
10 citations
07 Mar 2022
TL;DR: In this paper , the authors introduce the concept of synchronization bombs as large networks of heterogeneous oscillators that abruptly transit from incoherence to phaselocking by adding (or removing) one or a few links.
Abstract: Abstract Research on network percolation and synchronization has deepened our understanding of abrupt changes in the macroscopic properties of complex engineered and natural systems. While explosive percolation emerges from localized structural perturbations that delay the formation of a connected component, explosive synchronization is usually studied by fine-tuning of global parameters. Here, we introduce the concept of synchronization bombs as large networks of heterogeneous oscillators that abruptly transit from incoherence to phase-locking (or vice-versa) by adding (or removing) one or a few links. We build these bombs by optimizing global synchrony with decentralized information in a competitive percolation process driven by a local rule, and show their occurrence in systems of Kuramoto –periodic– and Rössler –chaotic– oscillators and in a model of cardiac pacemaker cells, providing an analytical characterization in the Kuramoto case. Our results propose a self-organized approach to design and control abrupt transitions in adaptive biological systems and electronic circuits, and place explosive synchronization and percolation under the same mechanistic framework.
3 citations
TL;DR: In this article , the authors introduce the concept of synchronization bombs as large networks of heterogeneous oscillators that abruptly transit from incoherence to phaselocking by adding (or removing) one or a few links.
Abstract: Abstract Research on network percolation and synchronization has deepened our understanding of abrupt changes in the macroscopic properties of complex engineered and natural systems. While explosive percolation emerges from localized structural perturbations that delay the formation of a connected component, explosive synchronization is usually studied by fine-tuning of global parameters. Here, we introduce the concept of synchronization bombs as large networks of heterogeneous oscillators that abruptly transit from incoherence to phase-locking (or vice-versa) by adding (or removing) one or a few links. We build these bombs by optimizing global synchrony with decentralized information in a competitive percolation process driven by a local rule, and show their occurrence in systems of Kuramoto –periodic– and Rössler –chaotic– oscillators and in a model of cardiac pacemaker cells, providing an analytical characterization in the Kuramoto case. Our results propose a self-organized approach to design and control abrupt transitions in adaptive biological systems and electronic circuits, and place explosive synchronization and percolation under the same mechanistic framework.
3 citations
References
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TL;DR: The advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology are reported and the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections are overviewed.
2,953 citations
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TL;DR: In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications.
Abstract: In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others We also survey and discuss existing data sets that can be represented as multilayer networks We review attempts to generalize single-layer-network diagnostics to multilayer networks We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks We conclude with a summary and an outlook
1,934 citations
TL;DR: It is shown that, in the infinite size limit, certain systems of globally coupled phase oscillators display low dimensional dynamics and an explicit finite set of nonlinear ordinary differential equations for the macroscopic evolution of the systems considered are derived.
Abstract: It is shown that, in the infinite size limit, certain systems of globally coupled phase oscillators display low dimensional dynamics. In particular, we derive an explicit finite set of nonlinear ordinary differential equations for the macroscopic evolution of the systems considered. For example, an exact, closed form solution for the nonlinear time evolution of the Kuramoto problem with a Lorentzian oscillator frequency distribution function is obtained. Low dimensional behavior is also demonstrated for several prototypical extensions of the Kuramoto model, and time-delayed coupling is also considered.
903 citations
TL;DR: In this article, B. Sonnenschein, E.R. dos Santos, P.J. Schultz, C.A. Ha, M.K. Choi and C.P.
683 citations
TL;DR: A review of the history of research on chimera states and major advances in understanding their behavior can be found in this article, where the authors highlight major advances on understanding their behaviour.
Abstract: A chimera state is a spatio-temporal pattern in a network of identical coupled oscillators in which synchronous and asynchronous oscillation coexist. This state of broken symmetry, which usually coexists with a stable spatially symmetric state, has intrigued the nonlinear dynamics community since its discovery in the early 2000s. Recent experiments have led to increasing interest in the origin and dynamics of these states. Here we review the history of research on chimera states and highlight major advances in understanding their behaviour.
593 citations