Related papers: Cluster synchronization of diffusively-coupled non…
Synchronization is a fundamental dynamical state of interacting oscillators, observed in natural biological rhythms and in the brain. Global synchronization which occurs when non-linear or chaotic oscillators placed on the nodes of a…
A network of propagating nonlinear oscillatory modes (waves) in the human brain is shown to generate collectively synchronized spiking activity (hypersynchronous spiking) when both amplitude and phase coupling between modes are taken into…
We present an extended analysis, based on the dynamics towards synchronization of a system of coupled oscillators, of the hierarchy of communities in complex networks. In the synchronization process, different structures corresponding to…
This article studies the synchronization problem of complex dynamical networks. The impulsive control method is considered with a novel event-triggered pinning algorithm. Sufficient conditions on the network topology are obtained to ensure…
Clustering and correlation effects are frequently observed in chaotic systems in situations where, because of the positivity of the Lyapunov exponents, no dimension reduction is to be expected. In this paper, using a globally coupled…
We consider models of identical pulse-coupled oscillators with global interactions. Previous work showed that under certain conditions such systems always end up in sync, but did not quantify how small clusters of synchronized oscillators…
To understand how certain dynamical behaviors can or cannot persist as the underlying network grows is a problem of increasing importance in complex dynamical systems as well as sustainability science and engineering. We address the…
The question under which conditions oscillators with slightly different frequencies synchronize appears in various settings. We show that synchronization can be achieved even for harmonic oscillators that are bilinearly coupled via a purely…
Coupled oscillator-based networks are an attractive approach for implementing hardware neural networks based on emerging nanotechnologies. However, the readout of the state of a coupled oscillator network is a difficult challenge in…
We study explosive synchronization, a phenomenon characterized by first-order phase transitions between incoherent and synchronized states in networks of coupled oscillators. While explosive synchronization has been the subject of many…
A network of chaotic systems can be designed in such a way that the cluster patterns formed by synchronous nodes can be controlled through the coupling parameters. We present a novel approach to exploit such a network for covert…
Synchronization in networks of oscillatory units is an emergent phenomenon present in various systems, such as biological, technological, and social systems. Many real-world systems have adaptive properties, meaning that their…
Synchronization in networks with delayed coupling are ubiquitous in nature and play a key role in almost all fields of science including physics, biology, ecology, climatology and sociology. In general, the published works on network…
Contraction metrics are crucial in control theory because they provide a powerful framework for analyzing stability, robustness, and convergence of various dynamical systems. However, identifying these metrics for complex nonlinear systems…
In this paper we address the problem of tracking control of nonlinear systems via contraction analysis. The necessary conditions of the systems which can achieve universal asymptotic tracking are studied under several different cases. We…
We study the popular distributed consensus method over networks composed of a number of densely connected clusters with a sparse connection between them. In these cluster networks, the method often constitutes two-time-scale dynamics, where…
Contraction analysis is a stability theory for nonlinear systems where stability is defined incrementally between two arbitrary trajectories. It provides an alternative framework in which to study uncertain interconnections or systems with…
We study the synchronization properties of a generic networked dynamical system, and show that, under a suitable approximation, the transition to synchronization can be predicted with the only help of eigenvalues and eigenvectors of the…
Dynamical balance of excitation and inhibition is usually invoked to explain the irregular low firing activity observed in the cortex. We propose a robust nonlinear balancing mechanism for a random network of spiking neurons, which works…
Reconstructing the states of the nodes of a dynamical network is a problem of fundamental importance in the study of neuronal and genetic networks. An underlying related problem is that of observability, i.e., identifying the conditions…