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Related papers: Pattern formation of a predator-prey system with I…

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Coupling diffusion process of signaling molecules with nonlinear interactions of intracellular processes and cellular growth/transformation leads to a system of reaction-diffusion equations coupled with ordinary differential equations…

Analysis of PDEs · Mathematics 2013-11-08 Anna Marciniak-Czochra , Madoka Nakayama , Izumi Takagi

In this work, we conduct a rigorous analysis on the dynamics of a predator-prey model with cooperative predation. From the root classification of an algebraic equation, we derive existence criteria of the positive equilibria. By Jacobian…

Classical Analysis and ODEs · Mathematics 2021-08-24 Srijana Ghimire , Xiang-Sheng Wang

Environmental enrichment can destabilize predator--prey coexistence through a Hopf bifurcation, yet real ecosystems are finite and intrinsically stochastic. We investigate how mechanistically derived demographic noise shapes near-Hopf…

Dynamical Systems · Mathematics 2026-03-18 Louis Shuo Wang , Jiguang Yu , Ye Liang , Jilin Zhang

Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…

Probability · Mathematics 2020-12-29 Lea Popovic , Liam Peuckert

Recently, a piecewise smooth differential system was derived as a model of a 1 predator-2 prey interaction where the predator feeds adaptively on its preferred prey and an alternative prey. In such a model, strong evidence of chaotic…

Dynamical Systems · Mathematics 2020-06-02 Tiago de Carvalho , Douglas Duarte Novaes , Luiz Fernando Gonçalves

Urban ecosystems exhibit complex predator-prey dynamics increasingly disrupted by anthropogenic disturbances (e.g., noise, habitat fragmentation). Classical Lotka-Volterra (LV) models fail to capture these human-induced stressors, and…

Populations and Evolution · Quantitative Biology 2025-09-24 Arhonefe Joseph Ogethakpo , Ozioma Ogoegbulem , Sarduana Joshua Apanapudor , Helen Onovwerosuoke Sanubi

In this paper, we investigate a Lotka-Volterra competition-diffusion system with self-memory effects and spatial heterogeneity under Dirichlet boundary conditions. We focus on how memory strength influences the coexistence and stability of…

Dynamical Systems · Mathematics 2025-04-22 Shu Li , Binxiang Dai

We study instabilities and pattern formation in reaction-diffusion layers that are diffusively coupled. For two-layer systems of identical two-component reactions, we analyze the stability of homogeneous steady states by exploiting the…

Pattern Formation and Solitons · Physics 2015-06-03 Anne J. Catlla , Amelia McNamara , Chad M. Topaz

Understanding how species persist under interacting stressors is a central challenge in ecology. We develop a spatially explicit reaction-diffusion framework to investigate competing species in landscapes shaped by climate variability,…

Populations and Evolution · Quantitative Biology 2026-02-02 Ton Viet Ta

Spatio-temporal pattern formation over the square and rectangular domain has received significant attention from researchers. A wide range of stationary and non-stationary patterns produced by two interacting populations is abundant in the…

Dynamical Systems · Mathematics 2022-08-10 Malay Banerjee , Swadesh Pal , Pranali Roy Chowdhury

Foraging movements of predator play an important role in population dynamics of prey-predator interactions, which have been considered as mechanisms that contribute to spatial self-organization of prey and predator. In nature, there are…

Dynamical Systems · Mathematics 2015-05-15 Yun Kang , Sourav Kumar Sasmal , Komi Messan

In this paper, I prove necessary and sufficient conditions for the existence of Turing instabilities in a general system with three interacting species. Turing instabilities describe situations when a stable steady state of a reaction…

Pattern Formation and Solitons · Physics 2024-05-24 Vit Piskovsky

Model studies indicate that many climate subsystems, especially ecosystems, may be vulnerable to 'tipping': a 'catastrophic process' in which a system, driven by gradually changing external factors, abruptly transitions (or 'collapses')…

Dynamical Systems · Mathematics 2025-06-30 Dock Staal , Arjen Doelman

The spatiotemporal patterns of a reaction diffusion mussel-algae system with a delay subject to Neumann boundary conditions is considered. The paper is a continuation of our previous studies on delay-diffusion mussel-algae model. The global…

Dynamical Systems · Mathematics 2018-07-26 Zuolin Shen , Junjie Wei

We study diffusion-driven pattern-formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing…

Physics and Society · Physics 2018-03-28 Andreas Brechtel , Philipp Gramlich , Daniel Ritterskamp , Barbara Drossel , Thilo Gross

Ecological systems are complex dynamical systems. Modelling efforts on ecosystems' dynamical stability have revealed that population dynamics, being highly nonlinear, can be governed by complex fluctuations. Indeed, experimental and field…

Dynamical Systems · Mathematics 2020-02-19 Lluís Alsedà , José Tomás Lázaro , Ricard Solé , Blai Vidiella , Josep Sardanyés

Enhancement of the predictive power and robustness of nonlinear population dynamics models allows ecologists to make more reliable forecasts about species' long term survival. However, the limited availability of detailed ecological data,…

Pattern Formation and Solitons · Physics 2025-04-18 Indrajyoti Gaine , Malay Banerjee

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

We investigate spreading properties of solutions of a large class of two-component reaction-diffusion systems, including prey-predator systems as a special case. By spreading properties we mean the long time behaviour of solution fronts…

Analysis of PDEs · Mathematics 2019-07-08 Arnaud Ducrot , Thomas Giletti , Hiroshi Matano

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…

Statistical Mechanics · Physics 2019-07-01 Shadisadat Esmaeili , Barton L. Brown , Michel Pleimling