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Related papers: Phase transition in a spatial Lotka-Volterra model

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Stochastic simulations of cyclic three-species spatial predator-prey models are usually performed in square lattices with nearest neighbor interactions starting from random initial conditions. In this Letter we describe the results of…

Populations and Evolution · Quantitative Biology 2018-04-20 P. P. Avelino , D. Bazeia , L. Losano , J. Menezes , B. F. de Oliveira

We study a normalized two dimensional competitive Lotka$-$Volterra system describing the interaction between state power and society power. Restricting attention to the positively invariant domain $[0,1]^2$, the analysis focuses on interior…

Dynamical Systems · Mathematics 2026-03-10 Kerime Nur Kavadar , Ali Demirci , Furkan Emre Isik

The random Lotka-Volterra model is widely used to describe the dynamical and thermodynamic features of ecological communities. In this work, we consider random symmetric interactions between species and analyze the strongly competitive…

Disordered Systems and Neural Networks · Physics 2022-02-22 Giulia Garcia Lorenzana , Ada Altieri

Two known distinct examples of one-dimensional systems which are known to exhibit a phase transition are critically examined: (A) a lattice model with harmonic nearest-neighbor elastic interactions and an on-site Morse potential, and (B)…

Statistical Mechanics · Physics 2007-06-17 N. Theodorakopoulos

Ecology and evolution under changing environments are important in many subfields of biology with implications for medicine. Here, we explore an example: the consequences of fluctuating environments on the emergence of antibiotic…

Populations and Evolution · Quantitative Biology 2021-04-13 Bryce Morsky , Dervis Can Vural

Cyclic predator-prey models with four or six species are studied on a square lattice when the invasion rates are varied. It is found that the cyclic invasions maintain a self-organizing pattern as long as the deviation of the invasion…

Populations and Evolution · Quantitative Biology 2008-01-21 Gyorgy Szabo , Attila Szolnoki

We study several variants of the stochastic four-state rock-paper-scissors game or, equivalently, cyclic three-species predator-prey models with conserved total particle density, by means of Monte Carlo simulations on one- and…

Populations and Evolution · Quantitative Biology 2010-11-13 Qian He , Mauro Mobilia , Uwe C. Täuber

We consider cyclic Lotka-Volterra models with three and four strategies where at every interaction agents play a strategy using a time-dependent probability distribution. Agents learn from a loss by reducing the probability to play a losing…

Statistical Mechanics · Physics 2015-05-25 Ben Intoy , Michel Pleimling

In this work we consider three species competing with each other in the same habitat. One of the species lives in the entire habitat, competing with the other two species, while the other two inhabit two disjoint regions of the habitat.…

Analysis of PDEs · Mathematics 2024-08-07 Pablo Álvarez-Caudevilla , Cristina Brändle , Mónica Molina-Becerra , Antonio Suárez

We study the spreading of families in two-dimensional multispecies predator-prey systems, in which species cyclically dominate each other. In each time step randomly chosen individuals invade one of the nearest sites of the square lattice…

Populations and Evolution · Quantitative Biology 2009-11-10 Maria Ravasz , Gyorgy Szabo , Attila Szolnoki

The spatial rock-scissors-paper game (or cyclic Lotka-Volterra system) is extended to study how the spatiotemporal patterns are affected by the constructed backgrounds providing uniform number of neighbors (degree) at each site. On the…

Statistical Mechanics · Physics 2009-11-10 Gyorgy Szabo , Attila Szolnoki , Rudolf Izsak

The Lotka-Volterra model reflects real ecological interactions where species compete for limited resources, potentially leading to coexistence, dominance of one species, or extinction of another. Comprehending the mechanisms governing these…

Analysis of PDEs · Mathematics 2024-10-01 Maicon Sonego , Enrique Zuazua

A five-species predator-prey model is studied on a square lattice where each species has two prey and two predators on the analogy to the Rock-Paper-Scissors-Lizard-Spock game. The evolution of the spatial distribution of species is…

Populations and Evolution · Quantitative Biology 2013-08-19 Jeromos Vukov , Attila Szolnoki , György Szabó

I present three models of plant--pathogen interactions. The models are stochastic and spatially explicit at the scale of individual plants. For each model, I use a version of pair approximation or moment closure along with a separation of…

Numerical Analysis · Mathematics 2025-10-20 David H. Brown

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

Spreading from a seed is studied by Monte Carlo simulation on a square lattice with two types of sites affecting the rates of birth and death. These systems exhibit a critical transition between survival and extinction. For time- dependent…

Disordered Systems and Neural Networks · Physics 2009-11-07 Gyorgy Szabo , Hajnalka Gergely , Beata Oborny

Large-scale Monte Carlo simulations of the bond-diluted three-dimensional 4-state Potts model are performed. The phase diagram and the physical properties at the phase transitions are studied using finite-size scaling techniques. Evidences…

Statistical Mechanics · Physics 2007-05-23 Christophe Chatelain , Bertrand Berche , Wolfhard Janke , Pierre-Emmanuel Berche

The nonequilibrium dynamics of a cycling three-state Potts model is studied on a square lattice using Monte Carlo simulations and continuum theory. This model is relevant to chemical reactions on a catalytic surface and to molecular…

Statistical Mechanics · Physics 2024-10-08 Hiroshi Noguchi , Jean-Baptiste Fournier

Nonequilibrium spatiotemporal patterns have been extensively studied. However, a single oscillator or cyclic loop of states is typically employed at each site in theories and simulations. Here, we investigate how competition among multiple…

Pattern Formation and Solitons · Physics 2026-03-10 Hiroshi Noguchi

We investigate the controllability of a generalized diffusive Lotka-Volterra competition model for two species, incorporating boundary controls and an interior multiplicative control. Considering a smooth, bounded N-dimensional domain, we…

Analysis of PDEs · Mathematics 2025-11-04 João Carlos Barreira , Maicon Sonego , Enrique Zuazua