Related papers: Slow-fast dynamics in stochastic Lotka-Volterra sy…
Understanding under what conditions interacting populations, whether they be plants, animals, or viral particles, coexist is a question of theoretical and practical importance in population biology. Both biotic interactions and…
Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics…
We study the long-time dynamics in non-Markovian single-population stochastic models, where one or more reactions are modelled as a stochastic process with a fat-tailed non-exponential distribution of waiting times, mimicking long-term…
We are interested in the long time behavior of a two-type density-dependent biological population conditioned to non-extinction, in both cases of competition or weak cooperation between the two species. This population is described by a…
We consider a stochastic model for the evolution of a discrete population structured by a trait with values on a finite grid of the torus, and with mutation and selection. Traits are vertically inherited unless a mutation occurs, and…
The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of…
We study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic…
The Fredkin spin chain serves as an interesting theoretical example of a quantum Hamiltonian whose ground state exhibits a phase transition between three distinct phases, one of which violates the area law. Here we consider a classical…
We present a numerical method for learning the dynamics of slow components of unknown multiscale stochastic dynamical systems. While the governing equations of the systems are unknown, bursts of observation data of the slow variables are…
In this work, we introduce an information-theoretic approach for considering changes in dynamics of finitely dimensional open quantum systems governed by master equations. This experimentally motivated approach arises from considering how…
In this paper, we study a system of stochastic partial differential equations with slow and fast time-scales, where the slow component is a stochastic real Ginzburg-Landau equation and the fast component is a stochastic reaction-diffusion…
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…
For most stochastic dynamical systems, variables which are tightly regulated tend to respond slowly to external changes. This idea is often discussed for applicable systems, within a linear response regime, through the Fluctuation…
For a population with any given number of types, we construct a new multivariate Moran process with frequency-dependent selection and establish, analytically, a correspondence to equilibrium Lotka-Volterra phenomenology. This…
We study a general class of interacting particle systems over a countable state space $V$ where on each site $x \in V$ the particle mass $\eta(x) \geq 0$ follows a stochastic differential equation. We construct the corresponding Markovian…
We propose a model based on coupled multiplicative stochastic processes to understand the dynamics of competing species in an ecosystem. This process can be conveniently described by a Fokker-Planck equation. We provide an analytical…
A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
This work is devoted to examining qualitative properties of dynamic systems, in particular, limit cycles of stochastic differential equations with both rapid switching and small diffusion. The systems are featured by multi-scale…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…