Abstract
This paper is concerned with stochastic reaction-diffusion kinetics governed by the reaction-diffusion master equation. Specifically, the primary goal of this paper is to provide a mechanistic basis of Turing pattern formation that is induced by intrinsic noise. To this end, we first derive an approximate reaction-diffusion system by using linear noise approximation. We show that the approximated system has a certain structure that is associated with a coupled dynamic multi-agent system. This observation then helps us derive an efficient computation tool to examine the spatial power spectrum of the intrinsic noise. We numerically demonstrate that the result is quite effective to analyze noise-induced Turing pattern. Finally, we illustrate the theoretical mechanism behind the noise-induced pattern formation with a H2 norm interpretation of the multi-agent system.
| Original language | English |
|---|---|
| Article number | 6426152 |
| Pages (from-to) | 1053-1058 |
| Number of pages | 6 |
| Journal | Unknown Journal |
| DOIs | |
| Publication status | Published - 2012 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Control and Systems Engineering
- Modelling and Simulation
- Control and Optimization
Cite this
Noise-induced spatial pattern formation in stochastic reaction-diffusion systems. / Hori, Yutaka; Hara, Shinji.
In: Unknown Journal, 2012, p. 1053-1058.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Noise-induced spatial pattern formation in stochastic reaction-diffusion systems
AU - Hori, Yutaka
AU - Hara, Shinji
PY - 2012
Y1 - 2012
N2 - This paper is concerned with stochastic reaction-diffusion kinetics governed by the reaction-diffusion master equation. Specifically, the primary goal of this paper is to provide a mechanistic basis of Turing pattern formation that is induced by intrinsic noise. To this end, we first derive an approximate reaction-diffusion system by using linear noise approximation. We show that the approximated system has a certain structure that is associated with a coupled dynamic multi-agent system. This observation then helps us derive an efficient computation tool to examine the spatial power spectrum of the intrinsic noise. We numerically demonstrate that the result is quite effective to analyze noise-induced Turing pattern. Finally, we illustrate the theoretical mechanism behind the noise-induced pattern formation with a H2 norm interpretation of the multi-agent system.
AB - This paper is concerned with stochastic reaction-diffusion kinetics governed by the reaction-diffusion master equation. Specifically, the primary goal of this paper is to provide a mechanistic basis of Turing pattern formation that is induced by intrinsic noise. To this end, we first derive an approximate reaction-diffusion system by using linear noise approximation. We show that the approximated system has a certain structure that is associated with a coupled dynamic multi-agent system. This observation then helps us derive an efficient computation tool to examine the spatial power spectrum of the intrinsic noise. We numerically demonstrate that the result is quite effective to analyze noise-induced Turing pattern. Finally, we illustrate the theoretical mechanism behind the noise-induced pattern formation with a H2 norm interpretation of the multi-agent system.
UR - http://www.scopus.com/inward/record.url?scp=84874278395&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84874278395&partnerID=8YFLogxK
U2 - 10.1109/CDC.2012.6426152
DO - 10.1109/CDC.2012.6426152
M3 - Article
AN - SCOPUS:84874278395
SP - 1053
EP - 1058
JO - Mathematical Social Sciences
JF - Mathematical Social Sciences
SN - 0165-4896
M1 - 6426152
ER -