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We here discretize a predator-prey model by standard Euler forward method and non-standard finite difference method and then compare their dynamic properties with the corresponding continuous-time model. We show that NSFD model preserves…
Most mechanistic predator-prey modelling has involved either parameterization from process rate data or inverse modelling. Here, we take a median road: we aim at identifying the potential benefits of combining datasets, when both population…
We address the question of an averaging principle for a general class of multi-scale hybrid predator-prey models. We consider prey-predator models where the kinetic of the prey population, described by a differential equation, is faster…
We consider the properties of a slow-fast prey-predator system in time and space. We first argue that the simplicity of prey-predator system is apparent rather than real and there are still many of its hidden properties that have been…
A reaction-diffusion Leslie-Gower predator-prey model, incorporating the fear effect and prey refuge, with Beddington-DeAngelis functional response, is introduced. A qualitative analysis of the solutions of the model and the stability…
The importance of the Allee effect in studying extinction vulnerability is widely recognized by researchers, and neglecting it could adversely impact the management of threatened or exploited populations [1]. In this article, we examine a…
We use food webs generated by a model to investigate the effects of deleting species on other species in the web and on the web as a whole. The model incorporates a realistic population dynamics, adaptive foragers and other features which…
Mathematical modeling based on time-delay differential equations is an important tool to study the role of delay in biological systems and to evaluate its impact on the asymptotic behavior of their dynamics. Delays are indeed found in many…
We develop a mathematical model of extinction and coexistence in a generic predator-prey ecosystem composed of two herbivores in asymmetrical competition and a hunter exerting a predatory pressure on both species. With the aim of…
The main goal of this paper is to provide an algorithm for the random sampling of Butcher trees and the probabilistic numerical solution of ordinary differential equations (ODEs). This approach complements and simplifies a recent approach…
Computer modelling for evolutionary systems consists in: 1) to store in the memory the individual features of each member of a large population; and 2) to update the whole system repeatedly, as time goes by, according to some prescribed…
We develop a set of equations to describe the population dynamics of many interacting species in food webs. Predator-prey interactions are non-linear, and are based on ratio-dependent functional responses. The equations account for…
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…
In this paper, we introduce a two-sex controlled branching model to describe the interaction between predator and prey populations with sexual reproduction. This process is a two-type branching process, where the first type corresponds to…
Predators often consume multiple prey and by mutually subsidizing a shared predator, the prey may reciprocally harm each other. When predation levels are high, this apparent competition can culminate in a prey species being displaced.…
This paper investigates the long-term dynamics of a reaction-diffusion predator-prey system subject to random environmental fluctuations modeled by Markovian switching. The model is formulated as a hybrid system of partial differential…
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…
It is proved the existence and uniqueness of the global positive solution to the system of stochastic differential equations describing a non-autonomous stochastic predator-prey model with a modified version of Leslie-Gower and Holling-type…
In this paper we consider a class of discrete time prey-predator models with three interacting species defined on the two-dimensional simplex. For some choices of parameters of the operator describing the evolution of the relative…
The current landscape in time-series forecasting is dominated by Transformer-based models. Their high parameter count and corresponding demand in computational resources pose a challenge to real-world deployment, especially for commercial…