TY - GEN

T1 - Semidefinite programming for Turing instability analysis in molecular communication networks

AU - Hori, Yutaka

AU - Miyazako, Hiroki

N1 - Funding Information:
Yutaka Hori is with Department of Applied Physics and Physico-Informatics, Keio University. 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa 223-8522, Japan. yhori@appi.keio.ac.jp. Hiroki Miyazako is with Department of Information Physics and Computing, The University of Tokyo. 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan. miyazako.hiroki@gmail.com. This work was supported in part by JSPS KAKENHI Grant Number JP18H01464.
Publisher Copyright:
© 2019 IEEE.

PY - 2019/12

Y1 - 2019/12

N2 - This paper proposes a computationally tractable algebraic condition for Turing instability, a type of local instability inducing self-organized spatial pattern formation, in molecular communication networks. The molecular communication networks consist of spatially distributed homogeneous compartments, or biological cells, that interact with neighbor compartments using a small number of diffusible chemical species. Thus, the underlying spatio-temporal dynamics of the system can be modeled by reaction-diffusion equations whose diffusion terms are zero for some chemical species. We show that the molecular communication networks are not Turing unstable if and only if certain polynomials are non-negative. This leads to sum-of-squares optimizations for Turing instability analysis. The proposed approach is capable of predicting the formation of spatial patterns in molecular communication networks based on the mathematically rigorous analysis of Turing instability.

AB - This paper proposes a computationally tractable algebraic condition for Turing instability, a type of local instability inducing self-organized spatial pattern formation, in molecular communication networks. The molecular communication networks consist of spatially distributed homogeneous compartments, or biological cells, that interact with neighbor compartments using a small number of diffusible chemical species. Thus, the underlying spatio-temporal dynamics of the system can be modeled by reaction-diffusion equations whose diffusion terms are zero for some chemical species. We show that the molecular communication networks are not Turing unstable if and only if certain polynomials are non-negative. This leads to sum-of-squares optimizations for Turing instability analysis. The proposed approach is capable of predicting the formation of spatial patterns in molecular communication networks based on the mathematically rigorous analysis of Turing instability.

UR - http://www.scopus.com/inward/record.url?scp=85082483538&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85082483538&partnerID=8YFLogxK

U2 - 10.1109/CDC40024.2019.9029976

DO - 10.1109/CDC40024.2019.9029976

M3 - Conference contribution

AN - SCOPUS:85082483538

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 1874

EP - 1880

BT - 2019 IEEE 58th Conference on Decision and Control, CDC 2019

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 58th IEEE Conference on Decision and Control, CDC 2019

Y2 - 11 December 2019 through 13 December 2019

ER -