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Related papers: Spatial stochastic predator-prey models

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In the framework of Lotka-Volterra dynamics with evolutionary parameter variation, it is shown that a system of two competing species which is evolutionarily unstable, if left to themselves, is stabilized by a commmon predator preying on…

Condensed Matter · Physics 2009-11-10 Taksu Cheon , Shigemi Ohta

The best-response dynamics is an example of an evolutionary game where players update their strategy in order to maximize their payoff. The main objective of this paper is to study a stochastic spatial version of this game based on the…

Probability · Mathematics 2014-07-28 Stephen Evilsizor , Nicolas Lanchier

Many existing studies on pattern formation in the reaction-diffusion systems rely on deterministic models. However, environmental noise is often a major factor which leads to significant changes in the spatiotemporal dynamics. In this…

Populations and Evolution · Quantitative Biology 2015-09-30 Anuj Kumar Sirohi , Malay Banerjee , Anirban Chakraborti

The Rock-Paper-Scissors (RPS) model successfully reproduces some of the main features of simple cyclic predator-prey systems with interspecific competition observed in nature. Still, lattice-based simulations of the spatial stochastic RPS…

Populations and Evolution · Quantitative Biology 2022-03-14 P. P. Avelino , B. F. de Oliveira , R. S. Trintin

The critical properties of a simple prey-predator model are revisited. For some values of the control parameters, the model exhibits a line of directed percolation like transitions to a single absorbing state. For other values of the…

Statistical Mechanics · Physics 2009-11-07 Tibor Antal , Michel Droz , Adam Lipowski , Geza Odor

We study the probability of fixation in a stochastic two-species competition model. By identifying a naturally occurring fast timescale, we derive an approximation to the associated backward Kolmogorov equation that allows us to obtain an…

Populations and Evolution · Quantitative Biology 2020-09-04 Glenn Young , Andrew Belmonte

We study a system of elliptic equations with strong competition and an arbitrary large number of components. The system is related to a model of predators and prey, with a single and where several predators compete with each other. In this…

Analysis of PDEs · Mathematics 2019-03-28 Henri Berestycki , Alessandro Zilio

In this letter we consider a single parameter generalization of the standard three species Rock-Paper-Scissors (RPS) model allowing for predator-prey reversal. This model, which shall be referred to as $\kappa$RPS model, incorporates…

Populations and Evolution · Quantitative Biology 2023-05-31 P. P. Avelino , B. F. de Oliveira , R. S. Trintin

Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…

Probability · Mathematics 2020-12-29 Lea Popovic , Liam Peuckert

Mathematical modeling and analysis of spatial-temporal population distributions of interacting species have gained significant attention in biology and ecology in recent times. In this work, we investigate a Bazykin-type prey-predator model…

Dynamical Systems · Mathematics 2023-06-22 Subrata Dey , Malay Banerjee , S. Ghorai

We analyze predator-prey dynamics in one dimension in which a Brownian predator adopts a chasing strategy that consists in stochastically resetting its current position to locations previously visited by a diffusive prey. We study three…

Disordered Systems and Neural Networks · Physics 2019-12-05 J. Quetzalcoatl Toledo-Marin , Denis Boyer , Francisco J. Sevilla

In this investigation we study the effects of climate change on predator-prey population dynamics. The interaction of predator and prey is described by the Variable Territory (VT) model with Allee effects in an Ordinary Differential…

Populations and Evolution · Quantitative Biology 2018-05-31 Sylvain Gretchko , Jessa Marley , Rebecca C. Tyson

The model of competition between densities of two different species, called predator and prey, is studied on a one dimensional periodic lattice, where each site can be in one of the four states say, empty, or occupied by a single predator,…

Statistical Mechanics · Physics 2011-06-02 Rakesh Chatterjee , P. K. Mohanty , Abhik Basu

In this paper, we study the dynamics of the ratio-dependent type prey-predator model with different free boundaries. The two free boundaries, determined by prey and predator respectively, implying that they may intersect each other as time…

Dynamical Systems · Mathematics 2021-05-13 Lingyu Liu

In this paper we study the dynamics of stochastic microorganism flocculation models. Given the strong influence of environmental and seasonal fluctuations that are present in these models, we propose a stochastic model that includes…

Probability · Mathematics 2025-11-18 Alexandru Hening , Nguyen T. Hieu , Dang H. Nguyen , Nhu Nguyen

We study a spatial predator-prey model in which prey can enter a protection zone (refuge) inaccessible to predators, while predators exhibit directed movement toward prey-rich regions. The directed movement is modeled by a far-sighted…

Analysis of PDEs · Mathematics 2026-01-23 Kousuke Kuto , Kazuhiro Oeda

We construct two ordinary-differential-equation models of a predator feeding adaptively on two prey types, and we evaluate the models' ability to fit data on freshwater plankton. We model the predator's switch from one prey to the other in…

Dynamical Systems · Mathematics 2018-09-19 Sofia H. Piltz , Lauri Harhanen , Mason A. Porter , Philip K. Maini

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

Understanding under what conditions interacting populations, whether they be plants, animals, or viral particles, coexist is a question of theoretical and practical importance in population biology. Both biotic interactions and…

Populations and Evolution · Quantitative Biology 2011-04-26 Sebastian J. Schreiber , Michel Benaïm , Kolawolé A. S. Atchadé

We investigate the optimal control of large-scale autonomous systems under explicitly adversarial conditions, incorporating the probabilistic destruction of agents over time. In many such systems, adversarial interactions arise as different…

Optimization and Control · Mathematics 2026-02-27 Claire Walton , Isaac Kaminer , Qi Gong , Abram H. Clark , Theodoros Tsatsanifos