Related papers: Similarity Between Two Stochastic Differential Sys…

Dynamical systems are ubiquitous and are often modeled using a non-linear system of governing equations. Numerical solution procedures for many dynamical systems have existed for several decades, but can be slow due to high-dimensional…

We study the asymptotic behavior of multiscale stochastic spatial gene networks. Multiscaling takes into account the difference of abundance between molecules , and captures the dynamic of rare species at a mesoscopic level. We introduce an…

Hybrid stochastic differential equations are a useful tool to model continuously varying stochastic systems which are modulated by a random environment that may depend on the system state itself. In this paper, we establish the pathwise…

This article is dedicated to the study and comparison of two chemostat-like competition models in a heterogeneous environment. The first model is a probabilistic model where we build a PDMP simulating the effect of the temporal…

From longitudinal biomedical studies to social networks, graphs have emerged as a powerful framework for describing evolving interactions between agents in complex systems. In such studies, after pre-processing, the data can be represented…

The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…

We characterize the identified sets of a wide range of stochastic choice models, including random utility, various models of boundedly-rational behavior, and dynamic discrete choice. In each of these settings, we show two distributions over…

We study a random dynamical system such that one transformation is randomly selected from a family of transformations and then applied on each iteration. For such random dynamical systems, we consider estimates of absolutely continuous…

Systems showing stochastic resonance (SR) or coherent resonance (CR) share some features, in particular the nearby periodic character of the signal. We show that in spite of this resemblance the different underlying dynamics can be detected…

Stochastic contact Hamiltonian systems are a class of important mathematical models, which can describe the dissipative properties with odd dimensions in the stochastic environment. In this article, we investigate the numerical dynamics of…

We propose models describing the collective dynamics of two opposing groups of individuals with stochastic communication. Individuals from the same group are assumed to align in a stochastic manner, while individuals from different groups…

In this work we bring out the existence of a novel kind of synchronization associated to the size of a complex system. A dichotomic random jump process associated to the dynamics of an externally driven stochastic system with $N$ coupled…

We show a data-driven approach to discover the underlying structural form of the mathematical equation governing the dynamics of multiple but similar systems induced by the same mechanisms. This approach hinges on theories that we lay out…

We propose an approach for testing the hypothesis that two realizations of the random variables in the form of histograms are taken from the same statistical population (i.e. that two histograms are drawn from the same distribution). The…

Adaptive dynamical systems arise in a multitude of contexts, e.g., optimization, control, communications, signal processing, and machine learning. A precise characterization of their fundamental limitations is therefore of paramount…

Matching dynamical systems, through different forms of conjugacies and equivalences, has long been a fundamental concept, and a powerful tool, in the study and classification of nonlinear dynamic behavior (e.g. through normal forms). In…

Ability of dynamical systems to relax to equilibrium has been investigated since the invention of statistical mechanics, which establishes the connection between dynamics of many-body Hamiltonian systems and phenomenological thermodynamics.…

We consider the modeling of the dynamics of the chemostat at its very source. The chemostat is classically represented as a system of ordinary differential equations. Our goal is to establish a stochastic model that is valid at the scale…

We study the statistical distribution of the closest encounter between generic smooth observations computed along different trajectories of a rapidly mixing dynamical system. At the limit of large trajectories, we obtain a distribution of…

We derive Markovian master equations of single and interacting harmonic systems in different scenarios, including strong internal coupling. By comparing the dynamics resulting from the corresponding Markovian master equations with exact…