Related papers: Fixed points of Boolean networks with sparse conne…
The number $\mathcal{N}$ of stable fixed points of locally coupled Kuramoto models depends on the topology of the network on which the model is defined. It has been shown that cycles in meshed networks play a crucial role in determining…
Synchronization is studied in a spatially-distributed network of weekly-coupled, excitatory neurons of Hodgkin-Huxley type. All neurons are coupled to each other synaptically with a fixed time delay and a coupling strength inversely…
We investigate two discrete models of excitable media on a one-dimensional integer lattice $\mathbb{Z}$: the $\kappa$-color Cyclic Cellular Automaton (CCA) and the $\kappa$-color Firefly Cellular Automaton (FCA). In both models, sites are…
We study the population profile in a simple discrete time model of population dynamics. Our model, which is closely related to certain ``bit-string'' models of evolution, incorporates competition for resources via a population dependent…
We investigate the number fluctuations of spatially split many-boson systems employing a theorem about the maximally and minimally attainable variances of an observable. The number fluctuations of many-boson systems are given for different…
We study the nonequilibrium phase transition in a model of aggregation of masses allowing for diffusion, aggregation on contact and fragmentation. The model undergoes a dynamical phase transition in all dimensions. The steady state mass…
Spatial fluctuations of the local electric field induced by a constant applied electric field in composite media are studied analytically and numerically. It is found that the density of states for the fields exhibit sharp peaks and abrupt…
Cooperative interactions pervade in a broad range of many-body populations, such as ecological communities, social organizations, and economic webs. We investigate the dynamics of a population of two equivalent species A and B that are…
Phase transitions not allowed in equilibrium steady states may happen however at the fluctuating level. We observe for the first time this striking and general phenomenon measuring current fluctuations in an isolated diffusive system. While…
We present a stochastic neural automata in which activity fluctuations and synaptic intensities evolve at different temperature, the latter moving through a set of stored patterns. The network thus exhibits various retrieval phases,…
In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in…
We develop a theory of fluctuations for Brownian systems with weak long-range interactions. For these systems, there exists a critical point separating a homogeneous phase from an inhomogeneous phase. Starting from the stochastic…
We consider the soft Boolean model, a model that interpolates between the Boolean model and long-range percolation, where vertices are given via a stationary Poisson point process. Each vertex carries an independent Pareto-distributed…
The fixed point that governs the critical behavior of magnets described by the $N$-vector chiral model under the physical values of $N$ ($N =2, 3$) is shown to be a stable focus both in two and three dimensions. Robust evidence in favor of…
In this work, we study the dynamical robustness in a system consisting of both active and inactive oscillators. We analytically show that the dynamical robustness of such system is determined by the cross link density between active and…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
In dynamical systems with distinct time scales the time evolution in phase space may be influenced strongly by the fixed points of the fast subsystem. Orbits then typically follow these points, performing in addition rapid transitions…
We consider point clouds obtained as random samples of a measure on a Euclidean domain. A graph representing the point cloud is obtained by assigning weights to edges based on the distance between the points they connect. Our goal is to…
Bootstrap percolation provides an emblematic instance of phase behavior characterised by an abrupt transition with diverging critical fluctuations. This unusual hybrid situation generally occurs in particle systems in which the occupation…
We proposed and theoretically studied a model of two separated spins coupled to a common bosonic bath. In our SU(2)-symmetric model, the phase transition point and the stable fixed point representing the nonclassical phase can be…