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We study a mathematical model of environments populated by both preys and predators, with the possibility for predators to actively compete for the territory. For this model we study existence and uniqueness of solutions, and their…

Analysis of PDEs · Mathematics 2022-12-06 Henri Berestycki , Alessandro Zilio

Mathematical modelling and numerical simulations of interaction populations are crucial topics in systems biology. The interactions of ecological models may occur among individuals of the same species or individuals of different species.…

Quantitative Methods · Quantitative Biology 2017-09-04 Sarbaz H. A. Khoshnaw

Many dynamical systems, such as the Lotka-Volterra predator-prey model and the Euler equations for the free rotation of a rigid body, are PT symmetric. The standard and well-known real solutions to such dynamical systems constitute an…

High Energy Physics - Theory · Physics 2008-11-26 Carl M. Bender , Darryl D. Holm , Daniel W. Hook

Physical systems that display competitive non-linear dynamics have played a key role in the development of mathematical models of Nature. Important examples include predator-prey models in ecology, biology, consumer-resource models in…

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

Simulation of population dynamics is a central research theme in computational biology, which contributes to understanding the interactions between predators and preys. Conventional mathematical tools of this theme, however, are incapable…

Multiagent Systems · Computer Science 2020-02-11 Jun Yamada , John Shawe-Taylor , Zafeirios Fountas

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

Stochastic, spatially extended models for predator-prey interaction display spatio-temporal structures that are not captured by the Lotka-Volterra mean-field rate equations. These spreading activity fronts reflect persistent correlations…

Statistical Mechanics · Physics 2024-05-09 Uwe C. Täuber

Including spatial structure and stochastic noise invalidates the classical Lotka-Volterra picture of stable regular population cycles emerging in models for predator-prey interactions. Growth-limiting terms for the prey induce a continuous…

Populations and Evolution · Quantitative Biology 2007-05-23 Mauro Mobilia , Ivan T. Georgiev , 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

In the present paper we reconsider the integrable case of the Hamiltonian $N$-species Volterra system, as it has been introduced by Vito Volterra in 1937 and significantly enrich the results already published in the ArXiv in 2019 by two of…

Exactly Solvable and Integrable Systems · Physics 2024-10-16 M. Scalia , O. Ragnisco , B. Tirozzi , F. Zullo

The two-species population dynamics model is the simplest paradigm of interspecies interaction. Here, we include intraspecific competition to the Lotka-Volterra model and solve it analytically. Despite being simple and thoroughly studied,…

Populations and Evolution · Quantitative Biology 2015-03-17 Brenno Caetano Troca Cabella , Alexandre Souto Martinez , Fabiano Ribeiro

Decision making is a fundamental capability of living organisms, and has recently been gaining increasing importance in many engineering applications. Here, we consider a simple decision-making principle to identify an optimal choice in…

Applied Physics · Physics 2020-03-27 Tomoaki Niiyama , Genki Furuhata , Atsushi Uchida , Makoto Naruse , Satoshi Sunada

Non-autonomous differential equations exhibit a highly intricate dynamics, and various concepts have been introduced to describe their qualitative behavior. In general, it is rare to obtain time dependent invariant compact attracting sets…

Dynamical Systems · Mathematics 2024-02-09 Juan Garcia-Fuentes , José A. Langa , Piotr Kalita , Antonio Suárez

We perform individual-based Monte Carlo simulations in a community consisting of two predator species competing for a single prey species, with the purpose of studying biodiversity stabilization in this simple model system. Predators are…

Populations and Evolution · Quantitative Biology 2018-07-11 Sheng Chen , Ulrich Dobramysl , Uwe C. Täuber

In this paper we investigate some free boundary problems for the Lotka-Volterra type prey-predator model in one space dimension. The main objective is to understand the asymptotic behavior of the two species (prey and predator) spreading…

Analysis of PDEs · Mathematics 2014-01-14 Mingxin Wang

Systems of interacting species, such as biological environments or chemical reactions, are often described mathematically by sets of coupled ordinary differential equations. While a large number $\beta$ of species may be involved in the…

Dynamical Systems · Mathematics 2024-01-17 Rebecca E. Morrison

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 study a Lotka-Volterra model which contains two prey and one predator with the Beddington-DeAngelis functional responses. First, we establish a set of sufficient conditions for existence of positive periodic solutions.…

Dynamical Systems · Mathematics 2015-08-31 Nguyen Thi Hoai Linh , Ta Hong Quang , Ta Viet Ton

The paper deals with a multiple species Lotka-Volterra model with infinite distributed delays and feedback controls, for which we assume a weak form of diagonal dominance of the instantaneous negative intra-specific terms over the infinite…

Classical Analysis and ODEs · Mathematics 2013-07-29 Teresa Faria , Yoshiaki Muroya