In this paper we give a complete description of the entire dynamics of the kinetic system of a reaction-diffusion system proposed by A. Gierer and H. Meinhardt. In particular, the α-limit sets and ω-limit sets of all trajectories are determined, and it is shown that the dynamics of the system exhibits various interesting behaviors, including convergent solutions, periodic solutions, unbounded oscillating global solutions, and finite time blow-up solutions.
Bibliographical noteFunding Information:
This research is supported in part by NSF, by the Grant-in-Aid for JSPS Fellows, The Ministry of Education, Culture, Sports, Science and Technology, Japan and by the Grant-in-Aid for Scientific Research (B), Japan Society for the Promotion of Science.
Copyright 2006 Elsevier B.V., All rights reserved.
- Kinetic system
- Reaction-diffusion system