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Related papers: A study on a class of predator-prey models with Al…

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In mathematical modeling, several different functional forms can often be used to fit a data set equally well, especially if the data is sparse. In such cases, these mathematically different but similar looking functional forms are…

Dynamical Systems · Mathematics 2022-08-08 Sarah K. Wyse , Maria M. Martignoni , May Anne Mata , Eric Foxall , Rebecca C. Tyson

We investigate the most probable phase portrait (MPPP) of a stochastic single-species model with the Allee effect using the non-local Fokker-Planck equation. This stochastic model is driven by non-Gaussian as well as Gaussian noise, and it…

Dynamical Systems · Mathematics 2023-02-03 Almaz Tesfay , Shenglan Yuan , Daniel Tesfay , James Brannan

In this paper we present analytical solution of a fractional order predator-prey model, where prey grows logistically and predation occurs following type II response function, by homotopy perturbation method. Numerical solutions are…

Dynamical Systems · Mathematics 2019-06-05 Shuvojit Mondal , Nandadulal Bairagi , Abhijit Lahiri

We construct exact solutions for a system of two nonlinear partial differential equations describing the spatio-temporal dynamics of a predator-prey system where the prey per capita growth rate is subject to the Allee effect. Using the…

Mathematical Physics · Physics 2015-06-11 R. A. Kraenkel , K. Manikandan , M. Senthilvelan

Inspired by an example of Grebogi et al [1], we study a class of model systems which exhibit the full two-step scenario for the nonautonomous Hopf bifurcation, as proposed by Arnold [2]. The specific structure of these models allows a…

Dynamical Systems · Mathematics 2013-05-08 Vasso Anagnostopoulou , Tobias Jäger , Gerhard Keller

Ratio-dependent predator-prey models have been increasingly favored by field ecologists where predator-prey interactions have to be taken into account the process of predation search. In this paper we study the conditions of the existence…

Dynamical Systems · Mathematics 2016-03-07 Shaban Aly , Imbunm Kim , Dongwoo Sheen

The method of generalized modeling has been applied successfully in many different contexts, particularly in ecology and systems biology. It can be used to analyze the stability and bifurcations of steady-state solutions. Although many…

Dynamical Systems · Mathematics 2015-03-06 Christian Kuehn , Thilo Gross

We propose and investigate a discrete-time predator-prey system with cooperative hunting in the predator population. The model is constructed from the classical Nicholson-Bailey host-parasitoid system with density dependent growth rate. A…

Dynamical Systems · Mathematics 2018-08-02 Yunshyong Chow , Sophia R. -J. Jang , Hua-Ming Wang

In this paper, we consider the diffusive Nicholson's blowflies model in spatially heterogeneous environment when the diffusion rate is large. We show that the ratio of the average of the maximum per capita egg production rate to that of the…

Dynamical Systems · Mathematics 2021-02-24 Dan Huang , Shanshan Chen

In this paper, an attempt is made to understand the dynamics of a three-dimensional discrete fractional-order eco-epidemiological model with Holling type II functional response. We first discretize a fractional-order predator-prey-parasite…

Dynamical Systems · Mathematics 2021-04-15 Shuvojit Mondal , Xianbing Cao , Nandadulal Bairagi

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…

Dynamical Systems · Mathematics 2023-04-26 Jaouad Danane , Delfim F. M. Torres

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…

Probability · Mathematics 2014-09-02 Alexandre Genadot

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

We study the adaptive dynamics of predator-prey systems modeled by a dynamical system in which the traits of predators and prey are allowed to evolve by small mutations. When only the prey are allowed to evolve, and the size of the…

Probability · Mathematics 2015-03-13 Rick Durrett , John Mayberry

The establishment and spreading of biological populations depends crucially on population growth at low densities. The Allee effect is a problem in those populations where the per-capita growth rate at low densities is reduced. We examine…

Statistical Mechanics · Physics 2011-04-12 Michael T. Gastner , Beata Oborny , Alexey B. Ryabov , Bernd Blasius

The strong Allee effect plays an important role on the evolution of population in ecological systems. One important concept is the Allee threshold that determines the persistence or extinction of the population in a long time. In general, a…

Analysis of PDEs · Mathematics 2024-08-05 Fanze Kong , Juncheng Wei

In this paper, conformal fractional order discretization [20, 24, 25] is used to analyze bifurcation analysis and stability of a predator-prey system. A continuous model has been discretized into a discrete one while preserving the…

Dynamical Systems · Mathematics 2025-02-07 Muhammad Rafaqat , Abubakar Masha , Nauman Ahmed , Ali Raza , Wojciech Sumelka

This paper is devoted to the study of a predator-prey model with predator-age structure that involves Michaelis-Menten type ratio-dependent functional response. We study some dynamical properties of the model by using the theory of…

Dynamical Systems · Mathematics 2017-11-07 Xiangming Zhang , Zhihua Liu

We study an individual-based predator-prey model of biological coevolution, using linear stability analysis and large-scale kinetic Monte Carlo simulations. The model exhibits approximate 1/f noise in diversity and population-size…

Populations and Evolution · Quantitative Biology 2007-06-13 Per Arne Rikvold , Volkan Sevim

The objective of this paper is to study the dynamical behaviour systematically of an ecological system with Beddington-DeAngelis functional response which avoids the criticism occurred in the case of ratio-dependent functional response at…

Dynamical Systems · Mathematics 2015-01-21 Sahabuddin Sarwardi , Md. Reduanur Mandal , Nurul Huda Gazi