相关论文: Coexistence and extinction for stochastic Kolmogor…
We study stochastic extinction for a class of Markov processes motivated by models in ecology and epidemiology. Extinction is often characterized by a boundedness condition and a condition on boundary Lyapunov exponents (invasion rates).…
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 develop a mathematical model of extinction and coexistence in a generic predator-prey ecosystem composed of two herbivores in asymmetrical competition and a hunter exerting a predatory pressure on both species. With the aim of…
Deterministic continuum models formulated in terms of non-local partial differential equations for the evolutionary dynamics of populations structured by phenotypic traits have been used recently to address open questions concerning the…
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…
Age-structured models capture the dynamic behavior of populations over time and result in nonlinear integro-partial differential equations (IPDEs). These processes arise in various fields such as biotechnology, economics, or demography.…
The paper concerns a class of $n$-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of ordinary differential equations. This family…
In numerous papers, the behaviour of stochastic population models is investigated through the sign of a real quantity which is the growth rate of the population near the extinction set. In many cases, it is proven that when this growth rate…
We develop a stochastic two-patch epidemic model with nonlinear recidivism to investigate infectious disease dynamics in heterogeneous populations. Extending a deterministic framework, we introduce stochasticity to account for random…
In this note, we study the long time behavior of Lotka-Volterra systems whose coefficients vary randomly. Benam and Lobry established that randomly switching between two environments that are both favorable to the same species may lead to…
Conventional wisdom suggests that environmental noise drives populations toward extinction. In contrast, we report a paradoxical phenomenon in which stochasticity reverses a deterministic tipping point, thereby preventing collapse. Using a…
In this paper, we inspect well-known population genetics and social dynamics models. In these models, interacting individuals, while participating in a self-organizing process, give rise to the emergence of complex behaviors and patterns.…
This survey concerns the study of quasi-stationary distributions with a specific focus on models derived from ecology and population dynamics. We are concerned with the long time behavior of different stochastic population size processes…
To describe population dynamics, it is crucial to take into account jointly evolution mechanisms and spatial motion. However, the models which include these both aspects, are not still well-understood. Can we extend the existing results on…
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…
Understanding under what conditions populations, whether they be plants, animals, or viral particles, persist is an issue of theoretical and practical importance in population biology. Both biotic interactions and environmental fluctuations…
Reaction-diffusion systems with a Lotka-Volterra-type reaction term, also known as competition-diffusion systems, have been used to investigate the dynamics of the competition among $m$ ecological species for a limited resource necessary to…
This paper presents a study of the two-predators-two-preys discrete-time Lotka-Volterra model with self- inhibition terms for preys with direct applications to ecological problems. Parameters in the model are modified so that each of them…
May and Leonard (SIAM J. Appl. Math 1975) introduced a three-species Lotka-Volterra type population model that exhibits heteroclinic cycling. Rather than producing a periodic limit cycle, the trajectory takes longer and longer to complete…
Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest…