A Hopf bifurcation in a three-component reaction-diffusion system with a chemorepulsion

2014 ◽  
Vol 8 ◽  
pp. 3939-3952
Author(s):  
YoonMee Ham
Keyword(s):  
Hopf Bifurcation ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Three Component Reaction

scholarly journals A Hopf Bifurcation in a Three-Component Reaction-Diffusion System with a Chemoattraction

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
YoonMee Ham ◽  
Sang-Gu Lee ◽  
Quoc Phong Vu
Keyword(s):  
Hopf Bifurcation ◽  
Reaction Diffusion ◽  
Stationary Solutions ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Interface Conditions ◽  
Three Component Reaction

We consider a three-component reaction-diffusion system with a chemoattraction. The purpose of this work is to analyze the chemotactic effects due to the gradient of the chemotactic sensitivity and the shape of the interface. Conditions for existence of stationary solutions and the Hopf bifurcation in the interfacial problem as the bifurcation parameters vary are obtained analytically.

Stability and Hopf Bifurcation of a Reaction–Diffusion System with Weak Allee Effect

2021 ◽  
Vol 31 (07) ◽  
pp. 2150098
Author(s):  
Jia-Long Yue ◽  
Zhan-Ping Ma
Keyword(s):  
Steady State ◽  
Hopf Bifurcation ◽  
Allee Effect ◽  
Reaction Diffusion ◽  
Steady State Solution ◽  
State Solution ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Three Component Reaction ◽  
Species Population

A delayed three-component reaction–diffusion system with weak Allee effect and Dirichlet boundary condition is considered. The existence and stability of the positive spatially nonhomogeneous steady-state solution are obtained via the implicit function theorem. Moreover, taking delay as the bifurcation parameter, the Hopf bifurcation near the spatially nonhomogeneous steady-state solution is proved to occur at a critical value. Especially, the direction of Hopf bifurcation is forward and the bifurcated periodic solutions are unstable. Finally, the general results are applied to four types of three-species population models with weak Allee effect in growth.

Butterfly Catastrophe for Fronts in a Three-Component Reaction–Diffusion System

2014 ◽  
Vol 25 (1) ◽  
pp. 87-129 ◽  
Author(s):  
Martina Chirilus-Bruckner ◽  
Arjen Doelman ◽  
Peter van Heijster ◽  
Jens D. M. Rademacher
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Three Component Reaction
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