Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 27, Issue 4, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127417500493
Keywords
Cross-diffusion; steady-state solution; Lyapunov-Schmidt reduction; Hopf bifurcation
Funding
- National Natural Science Foundation of P. R. China [11671123, 11271115]
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This paper is devoted to a reaction cross-diffusion system under Neumann boundary conditions. Firstly, the existence and multiplicity of spatially nonhomogeneous/homogeneous steady-state solutions are investigated by means of Lyapunov-Schmidt reduction. Next, the linear stability and Hopf bifurcations of homogeneous steady-state solutions are described in detail. In particular, the Hopf bifurcation direction and the stability of bifurcating time-periodic solutions are determined by using center manifold reduction and normal form theory. Finally, some of the main results are illustrated by an application to a predator-prey model with Allee effect and one-dimensional spatial domain Omega = (0, l pi).
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