The dynamics of a kinetic activator-inhibitor system

Wei Ming Ni, Kanako Suzuki, Izumi Takagi

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)426-465
Number of pages40
JournalJournal of Differential Equations
Issue number2
StatePublished - Oct 15 2006

Bibliographical note

Funding 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

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