Stability and Hopf Bifurcation in a Reaction–Diffusion Model with Chemotaxis and Nonlocal Delay Effect
2018 ◽
Vol 28
(04)
◽
pp. 1850046
◽
Keyword(s):
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.
2012 ◽
Vol 13
(4)
◽
pp. 1961-1977
◽
Keyword(s):
2019 ◽
Vol 45
◽
pp. 736-754
◽
Keyword(s):
2015 ◽
Vol 259
(4)
◽
pp. 1409-1448
◽
Keyword(s):
2018 ◽
Vol 467
(2)
◽
pp. 1080-1099
◽
Keyword(s):
Keyword(s):
2018 ◽
Vol 41
(17)
◽
pp. 7789-7803
◽
2010 ◽
Vol 217
(8)
◽
pp. 4234-4238
Keyword(s):