Local versus nonlocal interactions in a reaction-diffusion system of population dynamics

DOI10.4171/RLM/674zbMath1295.35073MaRDI QIDQ2509476

Tetiana Savitska, Fabio Punzo

Publication date: 28 July 2014

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

zbMATH Keywords

nonlocal termasymptotically stable solutionsTuring destabilization

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Reaction-diffusion equations (35K57) Developmental biology, pattern formation (92C15) Bifurcations in context of PDEs (35B32) Integro-partial differential equations (35R09) Pattern formations in context of PDEs (35B36)

Related Items (5)

Bifurcation results for a non-local elliptic equation with a nonlinear boundary condition ⋮ Positive solutions of a nonlocal singular elliptic equation by means of a non-standard bifurcation theory ⋮ Turing instability and coexistence in an extended Klausmeier model with nonlocal grazing ⋮ A variational approach for Kirchhoff-Carrier type non-local equation boundary value problems ⋮ Nonlocal singular elliptic system arising from the amoeba–bacteria population dynamics

Cites Work

• Unnamed Item
• Local vs. non-local interactions in population dynamics
• Coexistence problem for two competing species models with density- dependent diffusion
• Asymptotic behavior and stability of solutions of semilinear diffusion equations
• Instability results for reaction-diffusion equations with Neumann boundary conditions
• Bifurcation and stability of stationary solutions of nonlocal scalar reaction-diffusion equations
• Propagation of population pulses and fronts in a cell replication problem: Non-locality and dependence on the initial function
• Asymptotic behavior for a system describing epidemics with migration and spatial spread of infection
• Shadow systems and attractors in reaction-diffusion equations
• Global Structure of Bifurcating Solutions of Some Reaction-Diffusion Systems
• Blow-up in Nonlocal Reaction-Diffusion Equations
• Models for Predator-Prey Systems at Multiple Scales
• Travelling front solutions of a nonlocal Fisher equation
• On a nonlocal diffusion equation with discontinuous reaction
• Mathematical modeling of bacterial virulence and host-pathogen interactions in the Dictyostelium/Pseudomonas system

This page was built for publication: Local versus nonlocal interactions in a reaction-diffusion system of population dynamics