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Exact Solutions and Conservation Laws of the Joseph-Egri Equation with Power Law Nonlinearity Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Impulsive Control and Synchronization of Spatiotemporal Chaos in the Gray–Scott Model

Authors : Kexue Zhang, Xinzhi Liu, Wei-Chau Xie

Published in: Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science

Publisher: Springer International Publishing

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Abstract

This chapter investigates the impulsive control and synchronization problem of spatiotemporal chaos in the Gray–Scott model. Based on the Lyapunov function method, a class of pinning impulsive controller is designed to stabilize and synchronize the spatiotemporal chaos in the Gray–Scott model. The approach allows us to analyze the stability and synchronization problem of other spatiotemporal chaotic systems with the same structure. Numerical simulations are provided to illustrate the theoretical results.

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previous chapter Leading Unstable Linear Systems to Chaos by Chaos Entanglement
Literature
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Gray, P., Scott, S.K.: Autocatalytic reactions in the isothermal, continuous stirred reactor. Chem. Eng. Sci. 39(6), 1087–1097 (1984)CrossRef
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Khadra, A., Liu, X., Shen, X.: Impulsive control and synchronization of spatiotemporal chaos. Chaos Solitions Fractals 26(2), 615–636 (2005)MATHMathSciNetCrossRef
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Kyrychko, Y.N., Blyuss, K.B.: Control of spatio-temporal patterns in the Gray–Scott model. Chaos. 19(4), 04312–6 (2009)CrossRef
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Lu, J., Kurths, J., Cao, J., Mahdavi, N., Huang, C.: Synchronization control for nonlinear stochastic dynamic networks: pinning impulsive strategy. IEEE Trans. Neural Netw. Learn. Syst. 23(2), 285–292 (2012)CrossRef
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Nishiura, Y., Ueyama, D.: Spatio-temporal chaos for the Gray-scott model. Physica D 150(3–4), 137–162 (2001)MATHCrossRef
Metadata
Title
Impulsive Control and Synchronization of Spatiotemporal Chaos in the Gray–Scott Model
Authors
Kexue Zhang
Xinzhi Liu
Wei-Chau Xie
Copyright Year
2015
Book
Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science

Print ISBN: 978-3-319-12306-6

Electronic ISBN: 978-3-319-12307-3

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-12307-3_78

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