Synchronization in asymmetrically coupled networks with homogeneous oscillators (original) (raw)

Asymmetry-induced synchronization in oscillator networks

Physical review. E, 2017

A scenario has recently been reported in which in order to stabilize complete synchronization of an oscillator network-a symmetric state-the symmetry of the system itself has to be broken by making the oscillators nonidentical. But how often does such behavior-which we term asymmetry-induced synchronization (AISync)-occur in oscillator networks? Here we present the first general scheme for constructing AISync systems and demonstrate that this behavior is the norm rather than the exception in a wide class of physical systems that can be seen as multilayer networks. Since a symmetric network in complete synchrony is the basic building block of cluster synchronization in more general networks, AISync should be common also in facilitating cluster synchronization by breaking the symmetry of the cluster subnetworks.

Generalized synchronization in mutually coupled oscillators and complex networks

Physical Review E, 2012

We introduce a concept of generalized synchronization, able to encompass the setting of collective synchronized behavior for mutually coupled systems and networking systems featuring complex topologies in their connections. The onset of the synchronous regime is confirmed by the dependence of the system's Lyapunov exponents on the coupling parameter. The presence of a generalized synchronization regime is verified by means of the nearest neighbor method.

Synchronization in slowly switching networks of coupled oscillators

Scientific reports, 2016

Networks whose structure of connections evolves in time constitute a big challenge in the study of synchronization, in particular when the time scales for the evolution of the graph topology are comparable with (or even longer than) those pertinent to the units' dynamics. We here focus on networks with a slow-switching structure, and show that the necessary conditions for synchronization, i.e. the conditions for which synchronization is locally stable, are determined by the time average of the largest Lyapunov exponents of transverse modes of the switching topologies. Comparison between fast- and slow-switching networks allows elucidating that slow-switching processes prompt synchronization in the cases where the Master Stability Function is concave, whereas fast-switching schemes facilitate synchronization for convex curves. Moreover, the condition of slow-switching enables the introduction of a control strategy for inducing synchronization in networks with arbitrary structure ...

On the synchronization region in networks of coupled oscillators

2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512), 2004

The Master Stability Function (MSF) is a standard tool for the stability analysis of the synchronization manifold in a network of oscillators. In this paper, we study the properties of the MSF and we characterize the geometry of the synchronization region in the complex plane. Our findings are rather general, regardless of the oscillator specifics.

Synchronization Stability of Coupled Near-Identical Oscillator Network

Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, 2009

We derive variational equations to analyze the stability of synchronization for coupled nearidentical oscillators. To study the effect of parameter mismatch on the stability in a general fashion, we define master stability equations and associated master stability functions, which are independent of the network structure. In particular, we present several examples of coupled nearidentical Lorenz systems configured in small networks (a ring graph and sequence networks) with a fixed parameter mismatch and a large Barabasi-Albert scale-free network with random parameter mismatch. We find that several different network architectures permit similar results despite various mismatch patterns.

Experiments on synchronization in networks of nonlinear oscillators with dynamic links

Nonlinear Theory and Its Applications, IEICE, 2013

This paper presents experimental results on the characterization of dynamics and synchronization of networks of nonlinear oscillators with dynamic links. The results are obtained using a new experimental setup. Accurate evaluation of synchronization with dynamic coupling is reported, with reference to a network of Chua oscillators, each settled onto a periodic orbit. The observed synchronization levels, as function of the dynamic link parameters, give a picture of the synchronization area in parameter space which is in agreement with previous theoretical predictions.

Enhancing the stability of the synchronization of multivariable coupled oscillators

Physical Review E, 2015

Synchronization processes in populations of identical networked oscillators are in the focus of intense studies in physical, biological, technological and social systems. Here we analyze the stability of the synchronization of a network of oscillators coupled through different variables. Under the assumption of an equal topology of connections for all variables, the master stability function formalism allows assessing and quantifying the stability properties of the synchronization manifold when the coupling is transferred from one variable to another. We report on the existence of an optimal coupling transference that maximizes the stability of the synchronous state in a network of Rössler-like oscillators. Finally, we design an experimental implementation (using nonlinear electronic circuits) which grounds the robustness of the theoretical predictions against parameter mismatches, as well as against intrinsic noise of the system.

Synchronization of delay-coupled oscillator networks

Physics-Uspekhi, 2013

Research on the synchronization of delay-coupled oscillator networks is reviewed. A number of key research approaches using different models and methods are described, and major results obtained through their use are presented and generalized. The most characteristic properties of time-delay coupled systems are discussed.

Synchronization in oscillator networks: Switching topologies and non-homogeneous delays

2005

Abstract We investigate the problem of synchronization in oscillator networks when the delay inherent in such systems is taken into account. We first investigate a general Kuramoto-type model with heterogeneous time delays, both with a complete network as well as a nearest neighbor interaction, for which we propose conditions for synchronization around a rotating frequency. Then, we turn our attention to the problem of synchronization when the topologies are allowed to change.

Network Synchronization Revisited: Time Delays in Mutually Coupled Oscillators

IEEE Access, 2022

Coordinated and efficient operation in large, complex systems requires the synchronization of the rhythms of spatially distributed components. Such systems are the basis for critical infrastructure such as satellite navigation, mobile communications, and services like the precision time protocol and Universal Coordinated Time. Different concepts for the synchronization of oscillator networks have been proposed, in particular mutual synchronization without and hierarchical synchronization from a reference clock. Established network synchronization models in electrical engineering address the role of inevitable cross-coupling time delays for network synchronization. Mutual synchronization has been studied using linear approximations of the coupling functions of these models. We review previous work and present a general model in which we study synchronization taking into account nonlinearities and finite time delays. As a result, dynamical phenomena in networks of coupled electronic oscillators induced by time delays, such as the multistability and stabilization of synchronized states can be predicted and observed. We study the linear stability of nonlinear states and predict for which system parameters synchronized states can be stable. We use these results to discuss the implementation of mutual synchronization for complex system architectures. A key finding is that mutual synchronization can result in stable in-and anti-phase synchronized states in the presence of large time delays. We provide the condition for which such synchronized states are guaranteed to be stable. INDEX TERMS Synchronization, delay effects, systems engineering and theory, control theory, phase locked loops, mutual coupling.