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Related papers: Time-dependent localized patterns in a predator-pr…

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The method of generalized modeling has been applied successfully in many different contexts, particularly in ecology and systems biology. It can be used to analyze the stability and bifurcations of steady-state solutions. Although many…

Dynamical Systems · Mathematics 2015-03-06 Christian Kuehn , Thilo Gross

The formation of self-organized patterns and localized states are ubiquitous in Nature. Localized states containing trivial symmetries such as stripes, hexagons, or squares have been profusely studied. Disordered patterns with non-trivial…

Pattern Formation and Solitons · Physics 2022-02-09 Marcel G. Clerc , Sebastián Echeverría-Alar , Mustapha Tlidi

In this paper we extend previous results on convergent perturbative solutions of the Schroedinger equation of a class of periodically time-dependent two-level systems. The situation treated here is particularly suited for the investigation…

Mathematical Physics · Physics 2015-06-26 J. C. A. Barata , D. A. Cortez

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

We identify a geometric principle governing the location of Hopf and Bogdanov--Takens bifurcations in planar predator--prey systems. The prey coordinate of any coexistence equilibrium undergoing such a bifurcation lies between consecutive…

Dynamical Systems · Mathematics 2026-03-26 E. Chan-López , A. Martín-Ruiz , Víctor Castellanos

We investigate a specific reaction-diffusion system that admits a monostable pulled front propagating at constant critical speed. When a small parameter changes sign, the stable equilibrium behind the front destabilizes, due to essential…

Analysis of PDEs · Mathematics 2021-10-07 Louis Garénaux

It is proved the existence and uniqueness of the global positive solution to the system of stochastic differential equations describing a non-autonomous stochastic predator-prey model with a modified version of Leslie-Gower and Holling-type…

Probability · Mathematics 2021-02-15 Olga Borysenko , Oleksandr Borysenko

Fluids subject to both thermal and compositional variations can undergo doubly diffusive convection when these properties both affect the fluid density and diffuse at different rates. A variety of patterns can arise from these…

Fluid Dynamics · Physics 2024-01-04 J. Tumelty , C. Beaume , A. M. Rucklidge

We study a spatial predator-prey model in which prey can enter a protection zone (refuge) inaccessible to predators, while predators exhibit directed movement toward prey-rich regions. The directed movement is modeled by a far-sighted…

Analysis of PDEs · Mathematics 2026-01-23 Kousuke Kuto , Kazuhiro Oeda

We model intracellular regulatory dynamics with threshold-type state-dependent delay and investigate the effect of the state-dependent diffusion time. A general model which is an extension of the classic differential equation models with…

Dynamical Systems · Mathematics 2018-03-13 Qingwen Hu

In this work, we study the dynamics of a spatially heterogeneous single population model with the memory effect and nonlinear boundary condition. By virtue of the implicit function theorem and Lyapunov-Schmidt reduction, spatially…

Dynamical Systems · Mathematics 2024-03-25 Quanli Ji , Ranchao Wu , Tonghua Zhang

In this paper, we analyse a recently proposed predator-prey model with ratio dependence and Holling type III functional response, with particular emphasis on the dynamics close to extinction. By using Briot-Bouquet transformation we…

Populations and Evolution · Quantitative Biology 2023-05-09 K. B. Blyuss , Y. N. Kyrychko , O. B. Blyuss

A novel analysis of homogeneous nucleation of dislocations in sheared two-dimensional crystals described by periodized discrete elasticity models is presented. When the crystal is sheared beyond a critical strain $F=F_{c}$, the strained…

Materials Science · Physics 2008-05-09 I. Plans , A. Carpio , L. L. Bonilla

We explore a diffusive predator-prey system that incorporates the fear effect in advective environments. Firstly, we analyze the eigenvalue problem and the adjoint operator, considering Constant-Flux and Dirichlet (CF/D) boundary…

Dynamical Systems · Mathematics 2023-12-04 Daifeng Duan , Ben Niu , Yuan Yuan

This paper explores the classification of parameter spaces for reaction-diffusion systems of two chemical species on stationary domains. The dynamics of the system are explored both in the absence and presence of diffusion. The parameter…

Pattern Formation and Solitons · Physics 2017-01-19 Wakil Sarfaraz , Anotida Madzvamuse

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

For a Selkov--Schnakenberg model as a prototype reaction-diffusion system on two dimensional domains we use the continuation and bifurcation software pde2path to numerically calculate branches of patterns embedded in patterns, for instance…

Dynamical Systems · Mathematics 2013-10-16 Hannes Uecker , Daniel Wetzel

A wide variety of stationary or moving spatially localized structures is present in evolution problems on unbounded domains, governed by higher-than-second-order reversible spatial interactions. This work provides a generic unfolding in one…

Pattern Formation and Solitons · Physics 2022-08-09 P. Parra-Rivas , A. R. Champneys , F. Al-Sahadi , D. Gomila , E. Knobloch

We study numerically the cubic-quintic-septic Swift-Hohenberg (SH357) equation on bounded one-dimensional domains. Under appropriate conditions stripes with wave number $k\approx 1$ bifurcate supercritically from the zero state and form…

Pattern Formation and Solitons · Physics 2019-07-17 Edgar Knobloch , Hannes Uecker , Daniel Wetzel

In this paper we explore the eco-evolutionary dynamics of a predator-prey model, where the prey population is structured according to a certain life history trait. The trait distribution within the prey population is the result of interplay…

Populations and Evolution · Quantitative Biology 2019-03-27 József Z. Farkas , A. Yu. Morozov