相关论文: A classification of the dynamics of three-dimensio…

Infinite-dimensional stochastic differential equations (ISDEs) describing systems with an infinite number of particles are considered. Each particle undergoes a L\'evy process, and the interaction between particles is determined by the…

We use dynamical generating functionals to study the stability and size of communities evolving in Lotka-Volterra systems with random interaction coefficients. The size of the eco-system is not set from the beginning. Instead, we start from…

We study stochastic pairwise interaction network systems whereby a finite population of agents, identified with the nodes of a graph, update their states in response to both individual mutations and pairwise interactions with their…

We study the stochastic dynamics of a system of interacting species in a stochastic environment by means of a continuous-time Markov chain with transition rates depending on the state of the environment. Models of gene regulation in systems…

An ecosystem is a nonlinear dynamical system, its orbits giving rise to the observed complexity in the system. The diverse components of the ecosystem interact in discrete time to give rise to emergent features that determine the trajectory…

It is well-established that including spatial structure and stochastic noise in models for predator-prey interactions invalidates the classical deterministic Lotka-Volterra picture of neutral population cycles. In contrast, stochastic…

In this paper we study the long term dynamics of two prey species and one predator species. In the deterministic setting, if we assume the interactions are of Lotka-Volterra type (competition or predation), the long term behavior of this…

Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology,…

Populations of replicating entities frequently experience sudden or cyclical changes in environment. We explore the implications of this phenomenon via a environmental switching parameter in several common evolutionary dynamics models…

Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…

Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how 'bottom up', individual-based models can be…

We study the persistence and extinction of species in a simple food chain that is modelled by a Lotka-Volterra system with environmental stochasticity. There exist sharp results for deterministic Lotka-Volterra systems in the literature but…

Noise, through its interaction with the nonlinearity of the living systems, can give rise to counter-intuitive phenomena such as stochastic resonance, noise-delayed extinction, temporal oscillations, and spatial patterns. In this paper we…

In this paper, we study a two-dimensional process arising as the unique nonnegative solution to a system of two stochastic differential equations (SDEs) with mutually enhancing two-way interactions driven by independent Brownian motions and…

This work is devoted to studying the dynamics of a structured population that is subject to the combined effects of environmental stochasticity, competition for resources, spatio-temporal heterogeneity and dispersal. The population is…

This work proposes to model the space environment as a stochastic dynamic network where each node is a group of objects of a given class, or species, and their relationship is represented by stochastic links. A set of stochastic dynamic…

This paper investigates the long-term dynamics of a reaction-diffusion predator-prey system subject to random environmental fluctuations modeled by Markovian switching. The model is formulated as a hybrid system of partial differential…

It has recently been shown that structural conditions on the reaction network, rather than a 'fine-tuning' of system parameters, often suffice to impart 'absolute concentration robustness' on a wide class of biologically relevant,…

We are interested in modeling the Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions, in the specific scales of the biological framework of adaptive dynamics.…

Species extinction occurs regularly and unavoidably in ecological systems. The time scales for extinction can broadly vary and inform on the ecosystem's stability. We study the spatio-temporal extinction dynamics of a paradigmatic…