TY - GEN
T1 - Turing instability in reaction-diffusion systems with a single diffuser
T2 - 52nd IEEE Conference on Decision and Control, CDC 2013
AU - Miyazako, Hiroki
AU - Hori, Yutaka
AU - Hara, Shinji
PY - 2013
Y1 - 2013
N2 - Cooperative behaviors arising from bacterial cellto- cell communication can be modeled by reaction-diffusion equations having only a single diffusible component. This paper presents the following three contributions for the systematic analysis of Turing instability in such reaction-diffusion systems. (i) We first introduce a unified framework to formulate the reaction-diffusion system as an interconnected multiagent dynamical system. (ii) Then, we mathematically classify biologically plausible and implausible Turing instabilities and characterize them by the root locus of each agent's dynamics, or the local reaction dynamics. (iii) Using this characterization, we derive analytic conditions for biologically plausible Turing instability, which provide useful guidance for the design and the analysis of biological networks. These results are demonstrated on an extended Gray-Scott model with a single diffuser.
AB - Cooperative behaviors arising from bacterial cellto- cell communication can be modeled by reaction-diffusion equations having only a single diffusible component. This paper presents the following three contributions for the systematic analysis of Turing instability in such reaction-diffusion systems. (i) We first introduce a unified framework to formulate the reaction-diffusion system as an interconnected multiagent dynamical system. (ii) Then, we mathematically classify biologically plausible and implausible Turing instabilities and characterize them by the root locus of each agent's dynamics, or the local reaction dynamics. (iii) Using this characterization, we derive analytic conditions for biologically plausible Turing instability, which provide useful guidance for the design and the analysis of biological networks. These results are demonstrated on an extended Gray-Scott model with a single diffuser.
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U2 - 10.1109/CDC.2013.6760286
DO - 10.1109/CDC.2013.6760286
M3 - Conference contribution
AN - SCOPUS:84902326564
SN - 9781467357173
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 2671
EP - 2676
BT - 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 10 December 2013 through 13 December 2013
ER -