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Related papers: Lotka-Volterra systems with stochastic resetting

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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…

Probability · Mathematics 2018-06-04 Alexandru Hening , Dang H. Nguyen

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…

Probability · Mathematics 2008-11-04 Patrick Cattiaux , Sylvie Méléard

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…

Probability · Mathematics 2021-11-29 Alexandru Hening , Dang Nguyen , Nhu Nguyen , Harrison Watts

We consider a broad class of stochastic lattice predator-prey models, whose main features are overviewed. In particular, this article aims at drawing a picture of the influence of spatial fluctuations, which are not accounted for by the…

Populations and Evolution · Quantitative Biology 2011-12-20 Mauro Mobilia , Ivan T. Georgiev , Uwe C. Tauber

We study the general properties of stochastic two-species models for predator-prey competition and coexistence with Lotka-Volterra type interactions defined on a $d$-dimensional lattice. Introducing spatial degrees of freedom and allowing…

Populations and Evolution · Quantitative Biology 2007-06-07 Mauro Mobilia , Ivan T. Georgiev , Uwe C. Tauber

In this paper we present the simplest individual level model of predator-prey dynamics and show, via direct calculation, that it exhibits cycling behavior. The deterministic analogue of our model, recovered when the number of individuals is…

Populations and Evolution · Quantitative Biology 2009-11-11 A. J. McKane , T. J. Newman

We investigate the Lotka-Volterra model for predator-prey competition with a finite carrying capacity that varies periodically in time, modeling seasonal variations in nutrients or food resources. In the absence of time variability, the…

Pattern Formation and Solitons · Physics 2026-05-05 Mohamed Swailem , Alastair M. Rucklidge

Our study focuses on analyzing the behavior of a stochastic predator-prey model with a time delay and logistic growth of prey, influenced by L\'{e}vy noise. Initially, we establish the existence, uniqueness, and boundedness of a positive…

Dynamical Systems · Mathematics 2023-04-26 Jaouad Danane , Delfim F. M. Torres

In this paper, we consider the inverse problem of determining the coefficients of interaction terms within some Lotka-Volterra models, with support from boundary observation of its non-negative solutions. In the physical background, the…

Analysis of PDEs · Mathematics 2024-04-23 Yuhan Li , Hongyu Liu , Catharine W. K. Lo

We investigate the competing effects and relative importance of intrinsic demographic and environmental variability on the evolutionary dynamics of a stochastic two-species Lotka-Volterra model by means of Monte Carlo simulations on a…

Populations and Evolution · Quantitative Biology 2013-01-28 Ulrich Dobramysl , Uwe C. Tauber

In this work, we examine a kinetic framework for modeling the time evolution of size distribution densities of two populations governed by predator-prey interactions. The model builds upon the classical Boltzmann-type equations, where the…

Analysis of PDEs · Mathematics 2025-11-27 Andrea Bondesan , Marco Menale , Giuseppe Toscani , Mattia Zanella

We study a system of Fokker-Planck equations recently introduced to describe the temporal evolution of statistical distributions of population densities with predator-prey interactions. At the macroscopic level, the system recovers a…

Analysis of PDEs · Mathematics 2026-03-11 Giuseppe Toscani , Mattia Zanella

We introduce a new predator-prey model by replacing the growth and predation constant by a square matrix, and the population density as a population vector. The classical Lotka-Volterra model describes a population that either modulates or…

Populations and Evolution · Quantitative Biology 2024-12-31 Pico Gilman , Steven J. Miller , Daeyoung Son , Saad Waheed , Janine Wang

We first present a predator-prey model for two species and then extend the model to three species where the two predator species engage in mutualistic predation. Constant effort harvesting and the impact of by-catch issue are also…

Dynamical Systems · Mathematics 2020-09-03 Mohammad M. Amirian , I. N. Towers , Z. Jovanoski , Andrew J. Irwin

A non-periodic version of the one-predator two-prey system model presented in [L.T.H. Nguyen, Q.H. Ta, T.V. T\d{a}, Existence and stability of periodic solutions of a Lotka-Volterra system, SICE International Symposium on Control Systems,…

Dynamical Systems · Mathematics 2017-09-12 Linh Thi Hoai Nguyen , Quang Hong Ta , Ton Viet Ta

We propose a model for the dynamics of frequencies of a costly defense trait. More precisely, we consider Lotka-Volterra-type models involving a prey (or host) population consisting of two types and a predator (or parasite) population,…

Probability · Mathematics 2022-06-22 Martin Hutzenthaler , Felix Jordan , Dirk Metzler

The classical Lotka-Volterra predator-prey system is often used in species competition modeling. An exact, closed-form solution is derived when the natural growth rate of the prey species and decay rate of the predators are equal in…

Dynamical Systems · Mathematics 2023-03-17 Jean-Luc Boulnois

We carry out mathematical analyses, {\em \`{a} la} Helmholtz's and Boltzmann's 1884 studies of monocyclic Newtonian dynamics, for the Lotka-Volterra (LV) equation exhibiting predator-prey oscillations. In doing so a novel "thermodynamic…

Mathematical Physics · Physics 2015-11-05 Yi-An Ma , Hong Qian

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…

Populations and Evolution · Quantitative Biology 2018-10-17 Tobias Galla

Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes…

Populations and Evolution · Quantitative Biology 2012-05-08 A. Dobrinevski , E. Frey