Related papers: Coupled Dynamics on Networks
The dynamics of one-way coupled systems with discrete time is considered. The behavior of the coupled logistic maps is compared to the dynamics of maps obtained using the Poincare sectioning procedure applied to the coupled continuous-time…
Complex networks evolve and vary their structure as time goes by. In particular, the links in those networks have both a sign and a directionality. To understand their structural principles, we measure the network motifs, which are patterns…
This paper studies synchronization in coupled nonlinear dynamic networks with unknown parameters. Adaptation can be added to one or several elements in the network, while preserving the global synchronization conditions derived in…
Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a…
Ensembles of coupled nonlinear oscillators are a popular paradigm and an ideal benchmark for analyzing complex collective behaviors. The onset of cluster synchronization is found to be at the core of various technological and biological…
In this paper we consider networks of dynamical systems that evolve in synchrony and investigate how dynamical information from the synchronization dynamics can be effectively used to learn the network topology, i.e., identify the time…
We consider networks of coupled stochastic oscillators. When coupled we find strong collective oscillations, while each unit remains stochastic. In the limit (N\to \infty) we derive a system of integro-delay equations and show analytically…
It has been proposed that adaptation in complex systems is optimized at the critical boundary between ordered and disordered dynamical regimes. Here, we review models of evolving dynamical networks that lead to self-organization of network…
Most complex networks serve as conduits for various dynamical processes, ranging from mass transfer by chemical reactions in the cell to packet transfer on the Internet. We collected data on the time dependent activity of five natural and…
The relation between network structure and dynamics is determinant for the behavior of complex systems in numerous domains. An important long-standing problem concerns the properties of the networks that optimize the dynamics with respect…
Lattice models of coupled dynamical systems lead to a variety of complex behaviors. Between the individual motion of independent units and the collective behavior of members of a population evolving synchronously, there exist more…
Controlling complex networked systems to a desired state is a key research goal in contemporary science. Despite recent advances in studying the impact of network topology on controllability, a comprehensive understanding of the synergistic…
We study the dynamics of diffusion processes acting on directed multiplex networks, i.e., coupled multilayer networks where at least one layer consists of a directed graph. We reveal that directed multiplex networks may exhibit a faster…
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…
Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…
We study numerically the dynamics of a network of all-to-all-coupled, identical sub-networks consisting of diffusively coupled, non-identical FitzHugh--Nagumo oscillators. For a large range of within- and between-network couplings, the…
We introduce a framework to intertwine dynamical processes of different nature, each with its own distinct network topology, using a multilayer network approach. As an example of collective phenomena emerging from the interactions of…
Synchronous firing of neurons is thought to play important functional roles such as feature binding and switching of cognitive states. Although synchronization has mainly been investigated using model neurons with simple connection topology…
We present and analyze a topologically induced transition from ordered, synchronized to disordered dynamics in directed networks of oscillators. The analysis reveals where in the space of networks this transition occurs and its underlying…
Synchrony is one of the most common dynamical states emerging on networks. The speed of convergence towards synchrony provides a fundamental collective time scale for synchronizing systems. Here we study the asymptotic synchronization times…