Abstract
This chapter addresses the problems of asymptotic stability analysis and finite-time stability analysis for delayed reaction-diffusion GRNs, respectively.
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References
Busenberg, S., Mahaffy, J.: Interaction of spatial diffusion and delays in models of genetic control by repression. J. Mol. Biol. 22(3), 313–333 (1985)
Cao, B., Zhang, Q., Ye, M.: Exponential stability of impulsive stochastic genetic regulatory networks with time-varying delays and reaction-diffusion. Adv. Differ. Eqn. 2016 (Article No. 307, 2016)
Du, Y., Li, Y., Xu, R.: Stability analysis for impulsive stochastic reaction-diffusion differential system and its application to neural networks. J. Appl. Math. 2013 (Article ID 785141, 12 pages, 2013)
Fan, X., Zhang, X., Wu, L., Shi, M.: Finite-time stability analysis of reaction-diffusion genetic regulatory networks time-varying delays. IEEE/ACM Trans. Comput. Biol. Bioinf. 14(4), 868–879 (2017)
Han, Y., Zhang, X., Wang, Y.: Asymptotic stability criteria for genetic regulatory networks with time-varying delays and reaction-diffusion terms. Circuits Syst. Signal Process. 34(10), 3161–3190 (2015)
Han, Y.Y., Zhang, X.: Stability analysis for delayed regulatory networks with reaction-diffusion terms (in Chinese). J. Nat. Sci. Heilongjiang Univ. 31(1), 32–40 (2014)
Löfberg, J.: YAPLMI: a toolbox for modeling and optimization in MATLAB. In: Proceedings of the 2004 IEEE International Symposium on Computer Aided Control Systems Design (CACSD), pp. 284–289 (2004)
Ma, Q., Shi, G.D., Xu, S.Y., Zou, Y.: Stability analysis for delayed genetic regulatory networks with reaction-diffusion terms. Neural Comput. Appl. 20(4), 507–516 (2011)
Park, P.G., Ko, J.W., Jeong, C.: Reciprocally convex approach to stability of systems with time-varying delays. Automatica 47(1), 235–238 (2011)
Zhou, J.P., Xu, S.Y., Shen, H.: Finite-time robust stochastic stability of uncertain stochastic delayed reaction-diffusion genetic regulatory networks. Neurocomputing 74(17), 2790–2796 (2011)
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Zhang, X., Wang, Y., Wu, L. (2019). Stability Analysis for Delayed Reaction-Diffusion GRNs . In: Analysis and Design of Delayed Genetic Regulatory Networks. Studies in Systems, Decision and Control, vol 207. Springer, Cham. https://doi.org/10.1007/978-3-030-17098-1_6
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DOI: https://doi.org/10.1007/978-3-030-17098-1_6
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