In this paper we investigate the eﬀects of time delay and diffusion rate on the stability of the positive steady state for a competition diffusion system with distributed delay. We obtain the condition of instability of the positive uniform steady state. Regarding the time delay as bifurcation parameter, we reduce the original system on the center manifold and get the stability of the Hopf bifurcation periodic solutions. Finally, regarding the diﬀusion rate as a bifurcation parameter, we show that the onedimensional competition diﬀusion system with inﬁnite delay and Dirichlet boundary condition exhibits the spatiotemporal structures near the steady state of the system.
Cite this article
Yanbin Tang, Li Zhou, Hopf Bifurcation and Stability of a Competition Diﬀusion System with Distributed Delay. Publ. Res. Inst. Math. Sci. 41 (2005), no. 3, pp. 589–597DOI 10.2977/PRIMS/1145475224