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Related papers: Turing instability in a diffusive predator-prey mo…

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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

We investigate stationary states, including their existence and stability, in a class of nonlocal aggregation-diffusion equations with linear diffusion and symmetric nonlocal interactions. For the scalar case, we extend previous results by…

Analysis of PDEs · Mathematics 2025-10-14 José A. Carrillo , Yurij Salmaniw

We study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns…

Pattern Formation and Solitons · Physics 2015-06-05 Luis Mier-y-Teran-Romero , Brandon Lindley , Ira B. Schwartz

Reaction-diffusion processes across layered media arise in several scientific domains such as pattern-forming E. coli on agar substrates, epidermal-mesenchymal coupling in development, and symmetry-breaking in cell polarisation. We develop…

Pattern Formation and Solitons · Physics 2020-09-18 Andrew L. Krause , Václav Klika , Jacob Halatek , Paul K. Grant , Thomas E. Woolley , Neil Dalchau , Eamonn A. Gaffney

We describe the resulting spatiotemporal dynamics when a homogeneous equilibrium loses stability in a spatially extended system. More precisely, we consider reaction-diffusion systems, assuming only that the reaction kinetics undergo a…

Analysis of PDEs · Mathematics 2023-10-23 Montie Avery

This paper investigates a dynamical predator-prey interaction model that incorporates: (a) hunting cooperation among predators; (b) Allee effect in prey. We show all possible boundary and interior solutions. In order to analyze the…

Dynamical Systems · Mathematics 2019-12-03 Aaditya Kharel , Zhifu Xie , Huiqing Zhu , Michelle McCullum , Nick Burks

This paper examines a discrete predator-prey model that incorporates prey refuge and its detrimental impact on the growth of the prey population. Age structure is taken into account for predator species. Furthermore, juvenile hunting as…

Populations and Evolution · Quantitative Biology 2023-08-21 Debasish Bhattacharjee , Nabajit Ray , Dipam Das , Hemanta Kumar Sarmah

This paper explores a stochastic Gause predator-prey model with bounded or sub-linear functional response. The model, described by a system of stochastic differential equations, captures the influence of stochastic fluctuations on…

Populations and Evolution · Quantitative Biology 2024-09-10 Leon Alexander Valencia , Ph. D , Jorge Mario Ramirez Osorio , Jorge Andres Sanchez

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

Nonlocal interactions are ubiquitous in nature and play a central role in many biological systems. In this paper, we perform a bifurcation analysis of a widely-applicable advection-diffusion model with nonlocal advection terms describing…

Analysis of PDEs · Mathematics 2023-05-25 Valeria Giunta , Thomas Hillen , Mark A. Lewis , Jonathan R. Potts

Striped patterns are known to bifurcate in reaction-diffusion systems with differential isotropic diffusions at a supercritical Turing instability. In this paper we study the impact of weak anisotropy by directional advection on the…

Analysis of PDEs · Mathematics 2020-03-02 Jichen Yang , Jens D. M. Rademacher , Eric Siero

Reaction-diffusion systems with time-delay defined on complex networks have been studied in the framework of the emergence of Turing instabilities. The use of the Lambert W-function allowed us get explicit analytic conditions for the onset…

Statistical Mechanics · Physics 2016-08-03 Julien Petit , Malbor Asllani , Duccio Fanelli , Ben Lauwens , Timoteo Carletti

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

Turing instability in activator-inhibitor systems provides a paradigm of nonequilibrium pattern formation; it has been extensively investigated for biological and chemical processes. Turing pattern formation should furthermore be possible…

Adaptation and Self-Organizing Systems · Physics 2010-05-13 Hiroya Nakao , Alexander S. Mikhailov

It is well known that for reaction-diffusion systems with differential isotropic diffusions, a Turing instability yields striped solutions. In this paper we study the impact of weak anisotropy by directional advection on such solutions, and…

Analysis of PDEs · Mathematics 2020-03-09 Jichen Yang , Jens D. M. Rademacher , Eric Siero

Pattern formation from homogeneity is well-studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is nontrivial to separate observed spatial patterning due to inherent spatial heterogeneity from…

Pattern Formation and Solitons · Physics 2019-12-10 Andrew L. Krause , Václav Klika , Thomas E. Woolley , Eamonn A. Gaffney

Honest signals and cues have been observed as part of interspecific and intraspecific communication among animals. Recent theories suggest that existing signaling systems have evolved through natural selection imposed by predators. Honest…

Populations and Evolution · Quantitative Biology 2020-03-02 Ahd Mahmoud Al-Salman , Joseph Páez Chávez , Karunia Putra Wijaya

This paper develops stability and stabilization results for systems of fully coupled jump diffusions. Such systems frequently arise in numerous applications where each subsystem (component) is operated under the influence of other…

Probability · Mathematics 2021-08-23 Dang Nguyen , Duy Nguyen , Nhu Nguyen , George Yin

Pattern formation is ubiquitous in nature and the mechanism widely-accepted to underlay them is based on the Turing instability, predicted by Alan Turing decades ago. This is a non-trivial mechanism that involves nonlinear interaction terms…

Pattern Formation and Solitons · Physics 2024-12-19 Javier López-Pedrares , Marcos Suárez-Vázquez , Juan Pérez-Mercader , Alberto P. Muñuzuri

This study introduces an innovative framework for merging ecological and epidemiological modeling via the formulation of a sophisticated predator-prey model that addresses the intricacies of disease dynamics, the Allee effect, and defensive…

Dynamical Systems · Mathematics 2025-05-06 Kwadwo Antwi-Fordjour , Zachary Overton , Dylan Lee