Related papers: Analysis of Reaction-Diffusion Predator-Prey Syste…
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…
In this paper, we investigate the global boundedness, asymptotic stability and pattern formation of predator-prey systems with density-dependent preytaxis in a two-dimensional bounded domain with Neumann boundary conditions, where the…
In recent years there has been a growing interest in the study of the dynamics of stochastic populations. A key question in population biology is to understand the conditions under which populations coexist or go extinct. Theoretical and…
Understanding the interaction between turbulence and zonal flows is critical for modeling turbulence transport in fusion plasmas, often described through predator-prey dynamics. However, traditional deterministic models like the…
Intraspecific trait variation has been increasingly recognized as an important factor in determining species interaction and diversity. Eco-evolutionary models have studied the distribution of trait values within a population that changes…
We study an open problem of risk-sensitive portfolio allocation in a regime-switching credit market with default contagion. The state space of the Markovian regime-switching process is assumed to be a countably infinite set. To characterize…
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…
A diffusive predator-prey system with predator interference and Neumann boundary conditions is considered in this paper. We derive some results on the existence and nonexistence of nonconstant stationary solutions. It is shown that there…
In this study, we apply two pillars of Scientific Machine Learning: Neural Ordinary Differential Equations (Neural ODEs) and Universal Differential Equations (UDEs) to the Lotka Volterra Predator Prey Model, a fundamental ecological model…
We show that spatial models of simple predator-prey interactions predict that predator and prey numbers oscillate in time and space. These oscillations are not seen in the deterministic versions of the models, but are due to stochastic…
Cyclic predator-prey systems have been shown to give rise to rich, and novel, space-time patterns, as for example coarsening domains with non-trivial in-domain dynamics. In this work we study numerically the responses of a cyclic…
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…
In this paper, we analyse a recently proposed predator-prey model with ratio dependence and Holling type III functional response, with particular emphasis on the dynamics close to extinction. By using Briot-Bouquet transformation we…
The concept of cross diffusion is applied to some biological systems. The conditions for persistence and Turing instability in the presence of cross diffusion are derived. Many examples including: predator-prey, epidemics (with and without…
This manuscript considers a Neumann initial-boundary value problem for the predator-prey system $$ \left\{ \begin{array}{l} u_t = D_1 u_{xx} - \chi_1 (uv_x)_x + u(\lambda_1-u+a_1 v), \\[1mm] v_t = D_2 v_{xx} + \chi_2 (vu_x)_x +…
Differential diffusion is a source of instability in population dynamics systems when species diffuse with different rates. Predator-prey systems show this instability only under certain specific conditions, usually requiring Holling-type…
We consider the model of spatially distributed population consisting of two species with "\textsl{predator\,--\,prey}" interaction; each of the species occupies two stations. Transfer of individuals between the stations (migration) is not…
We study a stochastic lattice predator-prey system by means of Monte Carlo simulations that do not impose any restrictions on the number of particles per site, and discuss the similarities and differences of our results with those obtained…
Spatially dependent parameters of a two-component chaotic reaction-diffusion PDE model describing ocean ecology are observed by sampling a single species. We estimate model parameters and the other species in the system by…
In this paper, we consider a two-player two-strategy game with random payoffs in a population subdivided into $d$ demes, each containing $N$ individuals at the beginning of any given generation and experiencing local extinction and…