scholarly journals Singular limit for a reaction-diffusion-ODE system in a neolithic transition model

2021 ◽  
Vol 295 ◽  
pp. 39-69
Author(s):  
Ján Eliaš ◽  
Danielle Hilhorst ◽  
Masayasu Mimura ◽  
Yoshihisa Morita
Keyword(s):  
Reaction Diffusion ◽  
Singular Limit ◽  
Transition Model ◽  
Neolithic Transition ◽  
Ode System

scholarly journals Instability Induced by Cross-Diffusion in a Predator-Prey Model with Sex Structure

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Shengmao Fu ◽  
Lina Zhang
Keyword(s):  
Reaction Diffusion ◽  
Positive Equilibrium ◽  
Predator Prey ◽  
Sex Structure ◽  
Cross Diffusion ◽  
Predator Prey Model ◽  
Ode System ◽  
Prey Model ◽  
Weakly Coupled ◽  
Coupled Reaction

In this paper, we consider a cross-diffusion predator-prey model with sex structure. We prove that cross-diffusion can destabilize a uniform positive equilibrium which is stable for the ODE system and for the weakly coupled reaction-diffusion system. As a result, we find that stationary patterns arise solely from the effect of cross-diffusion.

Long-time shadow limit for a reaction–diffusion-ODE system

2021 ◽  
Vol 112 ◽  
pp. 106790
Author(s):  
Chris Kowall ◽  
Anna Marciniak-Czochra ◽  
Andro Mikelić
Keyword(s):  
Reaction Diffusion ◽  
Ode System ◽  
Long Time
Sign in / Sign up

Export Citation Format

Share Document