Related papers: Phase-locking in weakly heterogeneous neuronal net…
This paper presents a framework for the study of convergence when the nodes' dynamics may be both piecewise smooth and/or nonidentical across the network. Specifically, we derive sufficient conditions for global convergence of all node…
Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network's automorphism group,…
We consider the multitasking associative network in the low-storage limit and we study its phase diagram with respect to the noise level $T$ and the degree $d$ of dilution in pattern entries. We find that the system is characterized by a…
The dynamic stability of the Boolean networks representing a model for the gene transcriptional regulation (Kauffman model) is studied by calculating analytically and numerically the Hamming distance between two evolving configurations.…
The human organism is an integrated network where complex physiologic systems, each with its own regulatory mechanisms, continuously interact, and where failure of one system can trigger a breakdown of the entire network. Identifying and…
Ensembles of phase-oscillators are known to exhibit a variety of collective regimes. Here, we show that a simple mean-field model involving two heterogenous populations of pulse-coupled oscillators, exhibits, in the strong-coupling limit, a…
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…
Phase transitions constitute fundamental mechanisms underlying abrupt or qualitative changes in the collective dynamics of interacting units across a wide range of natural and engineered systems. In dynamical networks, such transitions lead…
Triggering a single additional spike in a cerebral cortical neuron was recently demonstrated to cause a cascade of extra spikes in the network that is likely to rapidly decorrelate the network's microstate. The mechanisms involved in this…
When identical oscillators are coupled together in a network, dynamical steady states are often assumed to reflect network symmetries. Here we show that alternative persistent states may also exist that break the symmetries of the…
We discuss synchronization in networks of neuronal oscillators which are interconnected via diffusive coupling, i.e. linearly coupled via gap junctions. In particular, we present sufficient conditions for synchronization in these networks…
We study chaotic synchronization in networks with time-delayed coupling. We introduce the notion of strong and weak chaos, distinguished by the scaling properties of the maximum Lyapunov exponent within the synchronization manifold for…
Recent studies on the evolutionary dynamics of the Prisoner's Dilemma game in scale-free networks have demonstrated that the heterogeneity of the network interconnections enhances the evolutionary success of cooperation. In this paper we…
In computer simulations of spiking neural networks, often it is assumed that every two neurons of the network are connected by a probability of 2\%, 20\% of neurons are inhibitory and 80\% are excitatory. These common values are based on…
We investigate the dynamics of a neural network where each neuron evolves according to the combined effects of deterministic integrate-and-fire dynamics and purely inhibitory coupling with K randomly-chosen "neighbors". The inhibition…
We study the dynamics of two neuronal populations weakly and mutually coupled in a multiplexed ring configuration. We simulate the neuronal activity with the stochastic FitzHugh-Nagumo (FHN) model. The two neuronal populations perceive…
The process of pattern formation for a multi-species model anchored on a time varying network is studied. A non homogeneous perturbation superposed to an homogeneous stable fixed point can amplify, as follows a novel mechanism of…
Phase transitions in equilibrium and nonequilibrium systems play a major role in the natural sciences. In dynamical networks, phase transitions organize qualitative changes in the collective behavior of coupled dynamical units. Adaptive…
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…
Robustness of network of networks (NON) has been studied only for dependency coupling (J.X. Gao et. al., Nature Physics, 2012) and only for connectivity coupling (E.A. Leicht and R.M. D Souza, arxiv:0907.0894). The case of network of n…