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Related papers: Coexistence Steady States in a Predator-Prey Model

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In this paper, a stage structured predator-prey model with general nonlinear type of functional response is established and analyzed. The state-dependent time delay (hereafter SDTD) is the time taken from predator's birth to its maturity,…

Dynamical Systems · Mathematics 2021-06-18 Qianqian Zhang , Yuan Yuan , Yunfei Lv , Shengqiang Liu

Numerical continuation is used to compute solution branches in a two-component reaction-diffusion model of Leslie--Gower type. %in the vicinity of a Turing-Hopf interaction. Two regimes are studied in detail. In the first, the homogeneous…

Dynamical Systems · Mathematics 2024-03-26 Fahad Al Saadi , Edgar Knobloch , Mark Nelson , Hannes Uecker

We investigate existence of stationary solutions to an aggregation/diffusion system of PDEs, modelling a two species predator-prey interaction. In the model this interaction is described by non-local potentials that are mutually…

Analysis of PDEs · Mathematics 2019-04-11 S. Fagioli , Y. Jaafra

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…

Populations and Evolution · Quantitative Biology 2020-01-01 Luciano Stucchi , Javier Galeano , Desiderio A. Vasquez

In this paper, we investigate the effect of dispersal and advection on the dynamics of a predator-prey model. More precisely, we show that the linear stability of the semi-trivial steady state is determined by the dispersal rate, the…

Analysis of PDEs · Mathematics 2023-01-05 Qi Wang

We analyse a modified May-Holling-Tanner predator-prey model considering an Allee effect in the prey and alternative food sources for predator. Additionally, the predation functional response or predation consumption rate is linear. The…

Dynamical Systems · Mathematics 2019-03-25 Claudio Arancibia-Ibarra

Allee effect in population dynamics has a major impact in suppressing the paradox of enrichment through global bifurcation, and it can generate highly complex dynamics. The influence of the reproductive Allee effect, incorporated in the…

Dynamical Systems · Mathematics 2023-07-17 Subrata Dey , S Ghorai , Malay Banerjee

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…

Dynamical Systems · Mathematics 2017-01-11 Shanshan Chen , Junjie Wei , Jinzhu Yu

In ecology, prey switching refers to a predator's adaptive change of habitat or diet in response to prey abundance. In this paper, we study piecewise-smooth models of predator-prey interactions with a linear trade-off in a predator's prey…

Populations and Evolution · Quantitative Biology 2016-10-26 S. H. Piltz , M. A. Porter , P. K. Maini

In this manuscript, we consider temporal and spatio-temporal modified Holling-Tanner predator-prey models with predator-prey growth rate as a logistic type, Holling type II functional response and alternative food sources for the predator.…

Dynamical Systems · Mathematics 2019-12-18 Claudio Arancibia-Ibarra , Michael Bode , José Flores , Graeme Pettet , Peter van Heijster

The dynamics of a prey-predator system with foraging facilitation among predators are investigated. The analysis involves the computation of many semi-algebraic systems of large degrees. We apply the pseudo-division reduction, real-root…

Dynamical Systems · Mathematics 2020-02-26 Yong Yao

In this paper, we investigate the emergence of a predator-prey model with Beddington-DeAngelis-type functional response and reaction-diffusion. We derive the conditions for Hopf and Turing bifurcation on the spatial domain. Based on the…

Populations and Evolution · Quantitative Biology 2008-01-08 Weiming Wang , Lei Zhang , Yakui Xue , Zhen Jin

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…

Populations and Evolution · Quantitative Biology 2023-02-08 Florinda Capone , Roberta De Luca , Isabella Torcicollo

In any reaction-diffusion system of predator-prey models, the population densities of species are determined by the interactions between them, together with the influences from the spatial environments surrounding them. Generally, the prey…

Analysis of PDEs · Mathematics 2016-12-07 Xiao He , Sining Zheng

We study the Bazykin predator-prey model with predator intraspecific interactions and ratio-dependent functional response and show the existence and stability of two interior equilibrium points. We prove that the model displays a wide range…

Dynamical Systems · Mathematics 2021-03-08 Claudio Arancibia-Ibarra , Pablo Aguirre , José Flores , Peter van Heijster

The global stability of the nonhomogeneous positive steady state solution to a diffusive Holling-Tanner predator-prey model in a heterogeneous environment is proved by using a newly constructed Lyapunov function and estimates of nonconstant…

Analysis of PDEs · Mathematics 2020-07-31 Wenjie Ni , Junping Shi , Mingxin Wang

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 investigate a discrete-time phytoplankton-zooplankton model that incorporates a linear predator functional response alongside a Holling-type toxin distribution. Both Holling type II and type III cases are considered, and…

Dynamical Systems · Mathematics 2025-05-28 Sobirjon Shoyimardonov

A deterministic two-species predator-prey model with prey herd behavior is considered incorporating mutual interference and the effect of fear. We provide guidelines to the dynamical analysis of biologically feasible equilibrium points. We…

Dynamical Systems · Mathematics 2022-12-20 Kwadwo Antwi-Fordjour , Rana D. Parshad , Hannah E. Thompson , Stephanie B. Westaway

In this paper, we study the dynamics of a discrete Kolmogorov predator-prey model with Ricker-type prey growth. We give the sufficient and necessary condition to guarantee the existence and uniqueness of the positive fixed point. Using the…

Dynamical Systems · Mathematics 2024-05-21 Lei Niu , Susu Wang