The dynamics of a kinetic activator-inhibitor system

Wei Ming Ni, Kanako Suzuki, Izumi Takagi

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)


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
Pages (from-to)426-465
Number of pages40
JournalJournal of Differential Equations
Issue number2
Publication statusPublished - 2006 Oct 15


  • Kinetic system
  • Reaction-diffusion system

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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