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Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the…

Adaptation and Self-Organizing Systems · Physics 2022-08-30 Anna Zincenko , Sergei Petrovskii , Vitaly Volpert

Mutual interference and prey refuge are important drivers of predator-prey dynamics. The "exponent" or degree of mutual interference has been under much debate in theoretical ecology. In the present work, we investigate the interplay of the…

Dynamical Systems · Mathematics 2021-09-13 Kwadwo Antwi-Fordjour , Rana D. Parshad , Matthew A. Beauregard

A new model to investigate environmental effects of genetically distinguishable predators is presented. The Holling type II response function, modelling feeding satiation, leads to persistent system's oscillations, as in classical…

Dynamical Systems · Mathematics 2014-03-19 Clara Viberti , Ezio Venturino

Classical models of pattern formation are based on diffusion-driven instability (DDI) of constant stationary solutions of reaction-diffusion equations, which leads to emergence of stable, regular Turing patterns formed around that…

Analysis of PDEs · Mathematics 2016-02-03 Steffen Härting , Anna Marciniak-Czochra , Izumi Takagi

This paper investigates the dynamical behaviors of a Holling type I Leslie-Gower predator-prey model where the predator exhibits an Allee effect and is subjected to constant harvesting. The model demonstrates three types of equilibrium…

Dynamical Systems · Mathematics 2025-04-03 Jianhang Xie , Changrong Zhu

The process of pattern formation for a multi-species model anchored on a time varying network is studied. A non homogeneous perturbation superposed to an homogeneous stable fixed point can amplify, as follows a novel mechanism of…

Statistical Mechanics · Physics 2017-10-11 Julien Petit , Ben Lauwens , Duccio Fanelli , Timoteo Carletti

The role of predator evasion mediated by chemical signaling is studied in a diffusive prey-predator model when prey-taxis is taken into account (model A) or not (model B) with taxis strength coefficients $\chi$ and $\xi$ respectively. In…

Analysis of PDEs · Mathematics 2021-07-06 Purnedu Mishra , Dariusz Wrzosek

We present studies for an individual based model of three interacting populations whose individuals are mobile in a 2D-lattice. We focus on the pattern formation in the spatial distributions of the populations. Also relevant is the…

Populations and Evolution · Quantitative Biology 2007-12-18 I. C. Charret , M. V. Carneiro

Analytically tracking patterns emerging from a small amplitude Turing instability to large amplitude remains a challenge as no general theory exists. In this paper, we consider a three component reaction-diffusion system with one of its…

Dynamical Systems · Mathematics 2023-11-06 Christopher Brown , Gianne Derks , Peter van Heijster , David J. B. Lloyd

A stochastic version of the Brusselator model is proposed and studied via the system size expansion. The mean-field equations are derived and shown to yield to organized Turing patterns within a specific parameters region. When determining…

Statistical Mechanics · Physics 2015-05-14 Tommaso Biancalani , Duccio Fanelli , Francesca Di Patti

We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially…

Pattern Formation and Solitons · Physics 2010-11-15 A. V. Straube , A. Pikovsky

This paper investigates pattern formation in reaction--diffusion systems with both diffusive and nondiffusive components, providing necessary and sufficient conditions for diffusion-driven instability (DDI) and establishing the existence of…

Analysis of PDEs · Mathematics 2026-05-07 Théo André , Szymon Cygan , Anna Marciniak-Czochra , Finn Münnich

Time delays, modelling the process of intracellular gene expression, have been shown to have important impacts on the dynamics of pattern formation in reaction-diffusion systems. In particular, past work has shown that such time delays can…

Pattern Formation and Solitons · Physics 2022-06-28 Alec Sargood , Eamonn A. Gaffney , Andrew L. Krause

We present a computational framework to investigate steady state distributions and perform stability analysis for random ordinary differential equations driven by parameter uncertainty. Using the nonlinear Rosenzweig McArthur predator prey…

Dynamical Systems · Mathematics 2026-03-05 Wolfgang Hoegele

This paper concerns pattern formation in a class of reaction-advection-diffusion systems modeling the population dynamics of two predators and one prey. We consider the biological situation that both predators forage along the population…

Analysis of PDEs · Mathematics 2016-10-26 Ke Wang , Qi Wang , Feng Yu

Turing (or double-diffusive) instabilities describe pattern formation in reaction-diffusion systems, and were proposed in 1952 as a potential mechanism behind pattern formation in nature, such as leopard spots and zebra stripes. Because the…

Materials Science · Physics 2020-04-29 M. W. Noble , M. R. Tonks , S. P. Fitzgerald

Gene expression time delays, modelling the complex biological processes of gene transcription and translation, have been shown to play an important role in cellular dynamics. Time delays, motivated by the gene expression process, can also…

Cell Behavior · Quantitative Biology 2022-02-24 Alec Sargood

The problem of Turing instabilities for a reaction-diffusion system defined on a complex Cartesian product networks is considered. To this end we operate in the linear regime and expand the time dependent perturbation on a basis formed by…

Statistical Mechanics · Physics 2014-12-23 Malbor Asllani , Daniel M. Busiello , Timoteo Carletti , Duccio Fanelli , Gwendoline Planchon

In this paper, we investigate the global boundedness, asymptotic stability and pattern formation of predator-prey systems with density-dependent preytaxis in a two-dimensional bounded domain with Neumann boundary conditions, where the…

Analysis of PDEs · Mathematics 2019-07-05 Hai-Yang Jin , Zhi-An Wang

Results are reported concerning the formation of spatial patterns in the two-species ratio-dependent predator-prey model driven by spatial colored-noise. The results show that there is a critical value with respect to the intensity of…

Populations and Evolution · Quantitative Biology 2009-11-13 Quan-Xing Liu , Zhen Jin