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We explore the complex dynamical behavior of two simple predator-prey models of biological coevolution that on the ecological level account for interspecific and intraspecific competition, as well as adaptive foraging behavior. The…

Populations and Evolution · Quantitative Biology 2009-11-28 Per Arne Rikvold

Stemming from the stochastic Lotka-Volterra or predator-prey equations, this work aims to model the spatial inhomogeneity by using stochastic partial differential equations (SPDEs). Compared to the classical models, the SPDE model is more…

Dynamical Systems · Mathematics 2019-11-21 N. N. Nhu , G. Yin

This paper concerns with the global dynamics of classical solutions to an important alarm-taxis ecosystem, which demonstrates the behaviors of prey that attract secondary predator when threatened by primary predator. And the secondary…

Analysis of PDEs · Mathematics 2023-06-23 Songzhi Li , Kaiqiang Wang

In this paper, we proposed a population model depicting the dynamics of a prey species showing group defence against a generalist predator. The group defence characteristic is represented by a non-monotonic functional response. We have…

Dynamical Systems · Mathematics 2022-09-09 R. R. Patra , S. Maitra , S. Kundu

Metapopulation models have been instrumental in demonstrating the ecological impact of landscape structure on the survival of a focal species in complex environments. However, extensions to multiple species with arbitrary dispersal networks…

Populations and Evolution · Quantitative Biology 2024-11-06 Prajwal Padmanabha , Giorgio Nicoletti , Davide Bernardi , Samir Suweis , Sandro Azaele , Andrea Rinaldo , Amos Maritan

A reaction-diffusion-advection predator-prey model with Holling type-II predator functional response is considered. We show the stability/instability of the positive steady state and the existence of a Hopf bifurcation when the diffusion…

Dynamical Systems · Mathematics 2022-12-09 Yihuan Sun , Shanshan Chen

We consider a reaction-diffusion model for a population structured in phenotype. We assume that the population lives in a heterogeneous periodic environment, so that a given phenotypic trait may be more or less fit according to the spatial…

Analysis of PDEs · Mathematics 2025-03-07 Nathanaël Boutillon , Luca Rossi

In this work, we investigate the system of three species ecological model involving one predator-prey subsystem coupling with a generalist predator with negative effect on the prey. Without diffusive terms, all global dynamics of its…

Dynamical Systems · Mathematics 2020-04-28 Fanfan Li , Zhenlai Han , Ting-Hui Yang

In this paper, we consider a stochastic ratio-dependent predator-prey model. We firstly prove the existence, uniqueness and positivity of the solutions. Then, the boundedness of moments of population are studied. Finally, we show the…

Probability · Mathematics 2015-09-01 Nguyen Thi Hoai Linh , Ta Viet Ton

This paper aims at understanding the longtime behaviors of a reducible cooperative system with nonlocal diffusions and different free boundaries, describing the interactions of two mutually beneficial species. Compared with the irreducible…

Analysis of PDEs · Mathematics 2025-01-03 Lei Li , Mingxin Wang

The outcome of competition among species is influenced by the spatial distribution of species and effects such as demographic stochasticity, immigration fluxes, and the existence of preferred habitats. We introduce an individual-based model…

Populations and Evolution · Quantitative Biology 2010-07-19 Simone Pigolotti , Massimo Cencini

Reaction-diffusion systems may lead to the formation of steady state heterogeneous spatial patterns, known as Turing patterns. Their mathematical formulation is important for the study of pattern formation in general and play central roles…

Pattern Formation and Solitons · Physics 2015-06-05 Lucas D. Fernandes , Marcus A. M. Aguiar

This paper is concerned with a diffusive predator-prey model with predator-taxis and prey-taxis. Based on the Schauder fixed point theorem, we prove the global existence, uniqueness and boundedness of the classical solutions under the…

Analysis of PDEs · Mathematics 2021-08-03 Jianping Wang , Mingxin Wang

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

We propose a novel predator-prey model that integrate two ecologically significant mechanisms: the Allee effect in the prey population and cooperative hunting behavior among predators. Building upon the Rosenzweig-MacArthur framework, our…

Dynamical Systems · Mathematics 2026-01-19 Yujie Gao , Ton Viet Ta

We study the influence of spatially varying reaction rates on a spatial stochastic two-species Lotka-Volterra lattice model for predator-prey interactions using two-dimensional Monte Carlo simulations. The effects of this quenched…

Statistical Mechanics · Physics 2008-12-18 Ulrich Dobramysl , Uwe C. Tauber

We investigate the survivor distributions of a spatially extended model of competitive dynamics in different geometries. The model consists of a deterministic dynamical system of individual agents at specified nodes, which might or might…

Quantitative Methods · Quantitative Biology 2015-11-24 J. M. Luck , A. Mehta

The diffusive Lotka-Volterra predator-prey model \begin{eqnarray*} \left\{ \begin{array}{rcll} u_t &=& \nabla\cdot \left[ d_1\nabla u + \chi v^2 \nabla \Big(\dfrac{u}{v}\Big)\right] +u(m_1-u+av), \qquad & x\in\Omega, \ t>0, \\ v_t &=&…

Analysis of PDEs · Mathematics 2022-03-29 Frederic Heihoff , Tomomi Yokota

We consider a broad class of stochastic lattice predator-prey models, whose main features are overviewed. In particular, this article aims at drawing a picture of the influence of spatial fluctuations, which are not accounted for by the…

Populations and Evolution · Quantitative Biology 2011-12-20 Mauro Mobilia , Ivan T. Georgiev , Uwe C. Tauber

In this paper, we investigate the emergence of a predator-prey system with Ivlev-type functional response and reaction-diffusion. We study how diffusion affects the stability of predator-prey coexistence equilibrium and derive the…

Populations and Evolution · Quantitative Biology 2008-01-08 Weiming Wang , Lei Zhang , Hailing Wang , Zhenqing Li