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We show that intrinsic noise can induce spatio-temporal phenomena such as Turing patterns and travelling waves in a Brusselator model with nonlocal interaction terms. In order to predict and to characterize these quasi-waves we analyze the…
In this paper I will review some basic aspects of the mechanism of stochastic resonance. Stochastic resonance was first introduced as a possible mechanism to explain long term climatic variation. Since then, there have been many…
We study the effect of stochastic wireless channel models on the connectivity of ad hoc networks. Unlike in the deterministic geometric disk model where nodes connect if they are within a certain distance from each other, stochastic models…
A dynamical network, a graph whose nodes are dynamical systems, is usually characterized by a large dimensional space which is not always accesible due to the impossibility of measuring all the variables spanning the state space. Therefore,…
We analyze general two-species stochastic models, of the kind generally used for the study of population dynamics. We show that the conditions for the stochastic (microscopic) model to display approximate sustained oscillatory behavior are…
The occurrence of stochastic resonance in bistable systems undergoing anomalous diffusions, which arise from density-dependent fluctuations, is investigated with emphasis on the analytical formulation of the problem as well as a possible…
Chemical reaction networks describe interactions between biochemical species. Once an underlying reaction network is given for a biochemical system, the system dynamics can be modelled with various mathematical frameworks such as continuous…
This paper is concerned with conditions for the existence of oscillations in gene regulatory networks with negative cyclic feedback, where time delays in transcription, translation and translocation process are explicitly considered. The…
We present computer-assisted methods for analyzing stochastic models of gene regulatory networks. The main idea that underlies this equation-free analysis is the design and execution of appropriately-initialized short bursts of stochastic…
Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterising stochastic effects in biochemical systems is essential to understand the complex dynamics of living…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
We study a system of two-mode stochastic oscillators coupled through their collective output. As a function of a relevant parameter four qualitatively distinct regimes of collective behavior are observed. In an extended region of the…
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…
A stochastic reaction-diffusion model is studied on a networked support. In each patch of the network two species are assumed to interact following a non-normal reaction scheme. When the interaction unit is replicated on a directed linear…
Mathematical models of reaction networks can exhibit very complex dynamics, including multistability, oscillations, and chaotic dynamics. On the other hand, under some additional assumptions on the network or on parameter values, these…
Resonance is a well-known phenomenon that happens in systems with second order dynamics. In this paper we address the fundamental question of making a network robust to signal being periodically pumped into it at or near a resonant…
In this study, we estimate parameters in stochastic oscillatory systems by developing a novel cost function. This function incorporates power spectral density, analytic signal, and position crossings, each weighted to capture distinct…
We show the existence of internal stochastic resonance in a microscopic stochastic model for the oscillating CO oxidation on single crystal surfaces. This stochastic resonance arises directly from the elementary reaction steps of the system…
Statistical analysis of social networks provides valuable insights into complex network interactions across various scientific disciplines. However, accurate modeling of networks remains challenging due to the heavy computational burden and…
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…