Stability of periodic solutions arising from Hopf bifurcation for a reaction-diffusion equation with time delay

2002 ◽  
pp. 125-141 ◽  
Author(s):  
Teresa Faria ◽  
Wenzhang Huang
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Diffusion Equation ◽  
Periodic Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation

scholarly journals On Asymptotic Behavior for Reaction Diffusion Equation with Small Time Delay

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Xunwu Yin
Keyword(s):  
Asymptotic Behavior ◽  
Time Delay ◽  
Diffusion Equation ◽  
Bounded Solution ◽  
Reaction Diffusion ◽  
Small Time ◽  
Reaction Diffusion Equation ◽  
Small Time Delay ◽  
Scalar Diffusion

We investigate the asymptotic behavior of scalar diffusion equation with small time delayut-Δu=f(ut,u(t-τ)). Roughly speaking, any bounded solution will enter and stay in the neighborhood of one equilibrium when the equilibria are discrete.

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