scholarly journals Pattern formation and Turing instability in an activator–inhibitor system with power-law coupling

2015 ◽  
Vol 419 ◽  
pp. 487-497 ◽  
Author(s):  
F.A. dos S. Silva ◽  
R.L. Viana ◽  
S.R. Lopes
Keyword(s):  
Pattern Formation ◽  
Power Law ◽  
Turing Instability ◽  
Inhibitor System ◽  
Activator Inhibitor

Hopf bifurcation in an activator–inhibitor system with network

2019 ◽  
Vol 98 ◽  
pp. 22-28
Author(s):  
Yanling Shi ◽  
Zuhan Liu ◽  
Canrong Tian
Keyword(s):  
Hopf Bifurcation ◽  
Inhibitor System ◽  
Activator Inhibitor

A HOPF BIFURCATION IN A FREE BOUNDARY PROBLEM DEPENDING ON THE SPATIAL AVERAGE OF AN ACTIVATOR

2003 ◽  
Vol 13 (10) ◽  
pp. 3135-3145 ◽  
Author(s):  
YOONMEE HAM
Keyword(s):  
Hopf Bifurcation ◽  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Spatial Average ◽  
Inhibitor System ◽  
A Free Boundary Problem ◽  
Dynamics Of Interfaces ◽  
Activator Inhibitor

We shall consider an activator–inhibitor system proposed by Radehaus [1990]. In this system, the activator is inhibited by not only the inhibitor but also its own spatial average. The purpose of this paper is to analyze the dynamics of interfaces in an interfacial problem which is reduced from the system in order to examine how this problem is different from an activator–inhibitor system [Ham-Lee et al., 1994].

scholarly journals Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Xinze Lian ◽  
Shuling Yan ◽  
Hailing Wang
Keyword(s):  
Time Delay ◽  
Pattern Formation ◽  
Turing Instability ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Predator Prey Model ◽  
Prey Model ◽  
Diffusion Controlled ◽  
The Stability ◽  
Self Replication

We consider the effect of time delay and cross diffusion on the dynamics of a modified Leslie-Gower predator-prey model incorporating a prey refuge. Based on the stability analysis, we demonstrate that delayed feedback may generate Hopf and Turing instability under some conditions, resulting in spatial patterns. One of the most interesting findings is that the model exhibits complex pattern replication: the model dynamics exhibits a delay and diffusion controlled formation growth not only to spots, stripes, and holes, but also to spiral pattern self-replication. The results indicate that time delay and cross diffusion play important roles in pattern formation.

Reply to Correspondence: No Oscillations in Real Activator–Inhibitor Systems in Accomplishing Pattern Formation

2012 ◽  
Vol 74 (10) ◽  
pp. 2268-2271
Author(s):  
Eamonn A. Gaffney ◽  
Nick A. M. Monk ◽  
Ruth E. Baker ◽  
S. Seirin Lee
Keyword(s):  
Pattern Formation ◽  
Activator Inhibitor
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