Soliton-like phenomena in one-dimensional cross-diffusion systems: a predator--prey pursuit and evasion example

DOI10.1016/j.physd.2004.06.004zbMath1057.92057arXivnlin/0406013OpenAlexW2092099334WikidataQ57940413 ScholiaQ57940413MaRDI QIDQ1888039

John Brindley, Arun V. Holden, M. A. Tsyganov, V. N. Biktashev

Publication date: 22 November 2004

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0406013

zbMATH Keywords

Population dynamicsPopulation taxis wavesWave-splitting

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Population dynamics (general) (92D25) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Ecology (92D40)

Related Items (11)

Fortune favours the brave: movement responses shape demographic dynamics in strongly competing populations ⋮ Pattern formation of a spatial predator-prey system ⋮ Unnamed Item ⋮ Global solution for a general cross-diffusion two-competitive-predator and one-prey system with predator-taxis ⋮ Global existence of solutions for an \(m\)-component cross-diffusion system with a 3-component case study ⋮ Dynamics and pattern formation of a diffusive predator–prey model with predator-taxis ⋮ Pursuit-evasion predator-prey waves in two spatial dimensions ⋮ Solitary waves in excitable systems with cross-diffusion ⋮ A Minimal Model of Pursuit-Evasion in a Predator-Prey System ⋮ Families of traveling impulses and fronts in some models with cross-diffusion ⋮ Study of cross-diffusion induced Turing patterns in a ratio-dependent prey-predator model via amplitude equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Model for chemotaxis
• Deterministic Brownian motion in the hypermeander of spiral waves
• Phase breaks and chaos in a chain of diffusively coupled oscillators
• A cross-diffusion model of forest boundary dynamics
• Directed movement of predators and the emergence of density-dependence in predator-prey models.
• Front propagation and segregation in a reaction-diffusion model with cross-diffusion
• Cellular pattern formation during Dictyostelium aggregation
• Spatiotemporal Complexity of Plankton and Fish Dynamics
• A new continuum model for suspensions of gyrotactic micro-organisms
• On Nonlinear Convective Dispersal Effects in an Interacting Population Model
• Patchiness in plankton populations
• Wavefront propagation in a competition equation with a new motility term modelling contact inhibition between cell populations
• Excitability, wave reflection, and wave splitting in a cubic autocatalysis reaction-diffusion system
• Equilibria, stability and excitability in a general class of plankton population models
• Different strategies of evolution in a predator-prey system

This page was built for publication: Soliton-like phenomena in one-dimensional cross-diffusion systems: a predator--prey pursuit and evasion example