Periodic traveling waves in a reaction–diffusion model with chemotaxis and nonlocal delay effect

2018 ◽  
Vol 467 (2) ◽  
pp. 1080-1099 ◽  
Author(s):  
Dong Li ◽  
Shangjiang Guo
Keyword(s):  
Diffusion Model ◽  
Traveling Waves ◽  
Reaction Diffusion ◽  
Delay Effect ◽  
Periodic Traveling Waves ◽  
Nonlocal Delay ◽  
Reaction Diffusion Model

Stability and Hopf Bifurcation in a Reaction–Diffusion Model with Chemotaxis and Nonlocal Delay Effect

2018 ◽  
Vol 28 (04) ◽  
pp. 1850046 ◽  
Author(s):  
Dong Li ◽  
Shangjiang Guo
Keyword(s):  
Hopf Bifurcation ◽  
Diffusion Model ◽  
Dirichlet Boundary ◽  
Reaction Diffusion ◽  
High Concentration ◽  
Delay Effect ◽  
One Dimensional ◽  
Nonlocal Delay ◽  
Reaction Diffusion Model ◽  
Steady State Solutions

Chemotaxis is an observed phenomenon in which a biological individual moves preferentially toward a relatively high concentration, which is contrary to the process of natural diffusion. In this paper, we study a reaction–diffusion model with chemotaxis and nonlocal delay effect under Dirichlet boundary condition by using Lyapunov–Schmidt reduction and the implicit function theorem. The existence, multiplicity, stability and Hopf bifurcation of spatially nonhomogeneous steady state solutions are investigated. Moreover, our results are illustrated by an application to the model with a logistic source, homogeneous kernel and one-dimensional spatial domain.

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