Related papers: Partial Synchronization on Complex Networks
Many complex networks are known to exhibit sudden transitions between alternative steady states with contrasting properties. Such a sudden transition demonstrates a network's resilience, which is the ability of a system to persist in the…
Revealing physical interactions in complex systems from observed collective dynamics constitutes a fundamental inverse problem in science. Current reconstruction methods require access to a system's model or dynamical data at a level of…
We consider synchronization of weighted networks, possibly with asymmetrical connections. We show that the synchronizability of the networks cannot be directly inferred from their statistical properties. Small local changes in the network…
A new mathematical model for complex neural networks of the partly diffusive Hindmasrh-Rose equations with boundary coupling is proposed. Through analysis of absorbing dynamics for the solution semiflow, the asymptotic synchronization of…
Explosive synchronization (ES) is nowadays a hot topic of interest in nonlinear science and complex networks. So far, it is conjectured that ES is rooted in the setting of specific microscopic correlation features between the natural…
We introduce a technique to detect and quantify local functional dependencies between coupled chaotic systems. The method estimates the fraction of locally syncronized configurations, in a pair of signals with an arbitrary state of global…
Determining conditions on the coupling strength for the synchronization in networks of interconnected oscillators is a challenging problem in nonlinear dynamics. While sophisticated mathematical methods have been used to derive conditions,…
The issue of synchronization in the power grid is receiving renewed attention, as new energy sources with different dynamics enter the picture. Global metrics have been proposed to evaluate performance and analyzed under highly simplified…
We analyze a class of stochastic processes, referred to as asynchronous and semi-anonymous dynamics (ASD), over directed labeled random networks. These processes are a natural tool to describe general best-response and noisy best-response…
Performance of standard processes over large distributed networks typically scales with the size of the network. For example, in planar topologies where nodes communicate with their natural neighbors, the scaling factor is $O(n)$, where $n$…
The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and…
Spatio-temporal network dynamics is an emergent property of many complex systems which remains poorly understood. We suggest a new approach to its study based on the analysis of dynamical motifs -- small subnetworks with periodic and…
Co-evolutionary adaptive mechanisms are not only ubiquitous in nature, but also beneficial for the functioning of a variety of systems. We here consider an adaptive network of oscillators with a stochastic, fitness-based, rule of…
The paper investigates the synchronization of a network of identical linear state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling…
In many real-world systems, partial synchronization is the dominant dynamical regime and, in systems such as the brain, is often accompanied by collective oscillations in which multiple overlapping modes interact to produce complex rhythmic…
The framework of mutually coupled oscillators on a network has served as a convenient tool for investigating the impact of various parameters on the dynamics of real-world systems. Compared to large networks of oscillators, minimal networks…
A great variety of nonlinear dissipative systems are known to host structures having a correlation range much shorter than the size of the system. The dynamics of these Localized Structures (LSs) have been investigated so far in situations…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
We consider the coupling between two networks, each having N nodes whose individual dynamics is modeled by a two-state master equation. The intra-network interactions are all to all, whereas the inter-network interactions involve only a…
In the past decade, synchronization on complex networks has attracted increasing attentions from various research disciplines. Most previous works, however, focus only on the dynamic behaviors of synchronization process in the stable…