Related papers: Delay-Controlled Heterogeneous Nucleation in Adapt…
Networks of globally coupled, noise activated, bistable elements with connection time delays are considered. The dynamics of these systems is studied numerically using a Langevin description and analytically using (1) a Gaussian…
We investigate cluster synchronization in coupled map networks in the presence of heterogeneous delays. We find that while parity of heterogeneous delays plays a crucial role in determining the phenomenon of cluster formation, the…
In epidemiological modelling, dynamics on networks, and in particular adaptive and heterogeneous networks have recently received much interest. Here we present a detailed analysis of a previously proposed model that combines heterogeneity…
There is growing recognition that the network structures arising from interactions between different entities in physical, social and biological systems fundamentally alter the evolutionary outcomes. Previous paradigm exploring evolutionary…
Models of the consensus of the individual state in social systems have been the subject of recent researches in the physics literature. We investigate how network structures coevolve with the individual state under the framework of social…
Networks of neural mass nodes with delayed interactions are increasingly being used as models for large-scale brain activity. To complement the growing number of computational studies of such networks, it is timely to develop new…
Networked dynamical systems, i.e., systems of dynamical units coupled via nontrivial interaction topologies, constitute models of broad classes of complex systems, ranging from gene regulatory and metabolic circuits in our cells to…
This work introduces a methodology for studying synchronization in adaptive networks with heterogeneous plasticity (adaptation) rules. As a paradigmatic model, we consider a network of adaptively coupled phase oscillators with…
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…
Neural networks rely on learning synaptic weights. However, this overlooks other neural parameters that can also be learned and may be utilized by the brain. One such parameter is the delay: the brain exhibits complex temporal dynamics with…
There are three key factors of a system of coupled oscillators that characterize the interaction among them: coupling (how to affect), delay (when to affect) and topology (whom to affect). For each of them, the existing work has mainly…
This paper proposes two nonlinear dynamics to solve constrained distributed optimization problem for resource allocation over a multi-agent network. In this setup, coupling constraint refers to resource-demand balance which is preserved at…
We study the synchronization of coupled dynamical systems on a variety of networks. The dynamics is governed by a local nonlinear map or flow for each node of the network and couplings connecting different nodes via the links of the…
In systems of coupled oscillators, the effects of complex signaling can be captured by time delays and phase shifts. Here, we show how time delays and phase shifts lead to different oscillator dynamics and how synchronization rates can be…
We study a network of spiking neurons with heterogeneous excitabilities connected via inhibitory delayed pulses. For globally coupled systems the increase of the inhibitory coupling reduces the number of firing neurons by following a Winner…
Realistic networks display heterogeneous transmission delays. We analyze here the limits of large stochastic multi-populations networks with stochastic coupling and random interconnection delays. We show that depending on the nature of the…
We study control of synchronization in weakly coupled oscillator networks by using a phase reduction approach. Starting from a general class of limit cycle oscillators we derive a phase model, which shows that delayed feedback control…
The onset of synchronization in networks of networks is investigated. Specifically, we consider networks of interacting phase oscillators in which the set of oscillators is composed of several distinct populations. The oscillators in a…
It is known that an identical delay in all transmission lines can destabilize macroscopic stationarity of a neural network, causing oscillation or chaos. We analyze the collective dynamics of a network whose intra-transmission delays are…
We present a novel mathematical model of heterogeneous cell proliferation where the total population consists of a subpopulation of slow-proliferating cells and a subpopulation of fast-proliferating cells. The model incorporates two…