Related papers: On the relationship between equilibria and dynamic…
We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively…
In a generalized framework, where multi-state and inter-state linkages are allowed, we derive a sufficient condition for the stability of synchronization in a network of chaotic attractors. This condition explicitly relates the network…
This study investigates the suitability of the annealed approximation in high-dimensional systems characterized by dense networks with quenched link disorder, employing models of coupled oscillators. We demonstrate that dynamic equations…
In statistical physics any given system can be either at an equilibrium or away from it. Networks are not an exception. Most network models can be classified as either equilibrium or growing. Here we show that under certain conditions there…
Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider…
The behavior of the network and its stability are governed by both dynamics of individual nodes as well as their topological interconnections. Attention mechanism as an integral part of neural network models was initially designed for…
Multistability is a common phenomenon which naturally occurs in complex networks. If coexisting attractors are numerous and their basins of attraction are complexly interwoven, the long-term response to a perturbation can be highly…
In a series of two papers, we investigate the large deviations and asymptotic behavior of stochastic models of brain neural networks with random interaction coefficients. In this first paper, we take into account the spatial structure of…
Collective chaos is shown to emerge, via a period-doubling cascade, from quasiperiodic partial synchronization in a population of identical inhibitory neurons with delayed global coupling. This system is thoroughly investigated by means of…
We discuss the breakdown of spatial coherence in networks of coupled oscillators with nonlocal interaction. By systematically analyzing the dependence of the spatio-temporal dynamics on the range and strength of coupling, we uncover a…
We study a general set of models of social network evolution and dynamics. The models consist of both a dynamics on the network and evolution of the network. Links are formed preferentially between 'similar' nodes, where the similarity is…
Quantum chaotic dynamics is obtained for a tight-binding model in which the energies of the atomic levels at the boundary sites are chosen at random. Results for the square lattice indicate that the energy spectrum shows a complex behavior…
This paper is a review dealing with the study of large size random recurrent neural networks. The connection weights are selected according to a probability law and it is possible to predict the network dynamics at a macroscopic scale using…
The paper examines the discrete-time dynamics of neuron models (of excitatory and inhibitory types) with piecewise linear activation functions, which are connected in a network. The properties of a pair of neurons (one excitatory and the…
The Naming Game is a model of non-equilibrium dynamics for the self-organized emergence of a linguistic convention or a communication system in a population of agents with pairwise local interactions. We present an extensive study of its…
Networks in nature do not act in isolation but instead exchange information, and depend on each other to function properly. An incipient theory of Networks of Networks have shown that connected random networks may very easily result in…
We study the dynamics of two symmetrically coupled populations of identical leaky integrate-and-fire neurons characterized by an excitatory coupling. Upon varying the coupling strength, we find symmetry-breaking transitions that lead to the…
Several approaches to cognition and intelligence research rely on statistics-based models testing, namely factor analysis. In the present work we exploit the emerging dynamical systems perspective putting the focus on the role of the…
Chaos provides many interesting properties that can be used to achieve computational tasks. Such properties are sensitivity to initial conditions, space filling, control and synchronization. Chaotic neural models have been devised to…
Synchronization and resonance on networks are some of the most remarkable collective dynamical phenomena. The network topology, or the nature and distribution of the connections within an ensemble of coupled oscillators, plays a crucial…