TY - JOUR
T1 - The dynamics of a kinetic activator-inhibitor system
AU - Ni, Wei Ming
AU - Suzuki, Kanako
AU - Takagi, Izumi
N1 - 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.
PY - 2006/10/15
Y1 - 2006/10/15
N2 - 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.
AB - 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.
KW - Kinetic system
KW - Reaction-diffusion system
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U2 - 10.1016/j.jde.2006.03.011
DO - 10.1016/j.jde.2006.03.011
M3 - Article
AN - SCOPUS:33747161280
VL - 229
SP - 426
EP - 465
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 2
ER -