The dynamics of a kinetic activator-inhibitor system

Wei Ming Ni; Kanako Suzuki; Izumi Takagi

doi:10.1016/j.jde.2006.03.011

The dynamics of a kinetic activator-inhibitor system

Wei Ming Ni
, Kanako Suzuki
, Izumi Takagi

School of Mathematics

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	426-465
Number of pages	40
Journal	Journal of Differential Equations
Volume	229
Issue number	2
DOIs	https://doi.org/10.1016/j.jde.2006.03.011
State	Published - 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.

Keywords

Kinetic system
Reaction-diffusion system

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10.1016/j.jde.2006.03.011

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title = "The dynamics of a kinetic activator-inhibitor system",

abstract = "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.",

keywords = "Kinetic system, Reaction-diffusion system",

author = "Ni, \{Wei Ming\} and Kanako Suzuki and Izumi Takagi",

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.",

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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

UR - https://www.scopus.com/pages/publications/33747161280

UR - https://www.scopus.com/pages/publications/33747161280#tab=citedBy

U2 - 10.1016/j.jde.2006.03.011

DO - 10.1016/j.jde.2006.03.011

M3 - Article

AN - SCOPUS:33747161280

SN - 0022-0396

VL - 229

SP - 426

EP - 465

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 2

ER -

The dynamics of a kinetic activator-inhibitor system

Abstract

Bibliographical note

Keywords

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