Related papers: Noisy heteroclinic networks
A two dimensional self-gravitating Hamiltonian model made by $N$ fully-coupled classical particles exhibits a transition from a collapsing phase (CP) at low energy to a homogeneous phase (HP) at high energy. From a dynamical point of view,…
In this paper we obtain uniform propagation estimates for systems of interacting diffusions. We adopt a general model, satisfying various conditions which ensure that the decay resulting from the internal dynamics term dominates the…
We study the asymptotic behavior for asymmetric neuronal dynamics in a network of linear Hopfield neurons. The interaction between the neurons is modeled by random couplings which are centered i.i.d. random variables with finite moments of…
We investigate the stability properties of discrete and hybrid stochastic nonlinear dynamical systems. More precisely, we extend the stochastic contraction theorems (which were formulated for continuous systems) to the case of discrete and…
A continuous train of irregularly spaced spikes, peculiar of homoclinic chaos, transforms into clusters of regularly spaced spikes, with quiescent periods in between (bursting regime), by feeding back a low frequency portion of the…
We explore the relation between the topological relevance of a node in a complex network and the individual dynamics it exhibits. When the system is weakly coupled, the effect of the coupling strength against the dynamical complexity of the…
Neural dynamics is determined by the transmission of discrete synaptic pulses (synaptic shot-noise) among neurons. However, the neural responses are usually obtained within the diffusion approximation modeling synaptic inputs as continuous…
We present an analytical framework that allows the quantitative study of statistical dynamic properties of networks with adaptive nodes that have memory and is used to examine the emergence of oscillations in networks with response…
We examine the heterogeneous responses of individual nodes in sparse networks to the random removal of a fraction of edges. Using the message-passing formulation of percolation, we discover considerable variation across the network in the…
Spreading phenomena essentially underlie the dynamics of various natural and technological networked systems, yet how spatiotemporal propagation patterns emerge from such networks remains largely unknown. Here we propose a novel approach…
We consider a generic class of gene circuits affected by nonlinear extrinsic noise. To address this nonlinearity we introduce a general perturbative methodology based on assuming timescale separation between noise and genes dynamics, with…
A recurrent neural network with noisy input is studied analytically, on the basis of a Discrete Time Master Equation. The latter is derived from a biologically realizable learning rule for the weights of the connections. In a numerical…
Flow networks can describe many natural and artificial systems. We present a model for a flow system that allows for volume accumulation, includes conduits with a non-linear relation between current and pressure difference, and can be…
The rapidly increasing complexity of (mainly wireless) ad-hoc networks stresses the need of reliable distributed estimation of several variables of interest. The widely used centralized approach, in which the network nodes communicate their…
We study the dynamics of discrete-time regulatory networks on random digraphs. For this we define ensembles of deterministic orbits of random regulatory networks, and introduce some statistical indicators related to the long-term dynamics…
Transportation and distribution networks are a class of spatial networks that have been of interest in recent years. These networks are often characterized by the presence of complex structures such as central loops paired with peripheral…
Discrete dynamic models are a powerful tool for the understanding and modeling of large biological networks. Although a lot of progress has been made in developing analysis tools for these models, there is still a need to find approaches…
In shear flows at transitional Reynolds numbers, localized patches of turbulence, known as puffs, coexist with the laminar flow. Recently, Avila et al., Phys. Rev. Let. 110, 224502 (2013) discovered two spatially localized relative periodic…
We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in…
We consider the influence of local noise on a generalized network of populations having positive and negative feedbacks. The population dynamics at the nodes is nonlinear, typically chaotic, and allows cessation of activity if the…