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The Complex Geometry of the Mandelbrot Set Read chapter Read first chapter

2014 | OriginalPaper | Chapter

Adaptive Numerical Simulations of Reaction-Diffusion Systems with Time-Delayed Feedback

Authors : Dmitry Bratsun, Andrey Zakharov

Published in: ISCS 2013: Interdisciplinary Symposium on Complex Systems

Publisher: Springer Berlin Heidelberg

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Abstract

A new algorithm for calculating the dynamics of spatially-extended reaction-diffusion systems where the current state depends on the whole or partial previous evolution of the system is proposed. The algorithm is based on a finite difference method and involves an adaptive optimization of data storage by storing in a computer memory not all previous nodal data, but only some selected of them, called the base states. The intermediate states are restored by interpolation between the base states. The use of this technique allows the numerical calculations to be implemented on computer systems without large RAM memory. The algorithm efficiency is shown in three numerical examples.

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previous chapter Deterministic Modeling Spatio-Temporal Dynamics of Delay-Induced Circadian Oscillations in Neurospora crassa
next chapter Extracting the QRS Complexity and R Beats in Electrocardiogram Signals Using the Hilbert Transform
Literature
1.
Lakshmanan, M., Senthilkumar, D.V.: Dynamics of Nonlinear Time-Delay Systems. Springer, Berlin (2010)MATH
2.
3.
Bratsun, D.A.: Effect of unsteady forces on the stability of non-isothermal particulate flow under finite-frequency vibrations. Microgravity Sci. Technol. 21, 153–158 (2009)CrossRef
4.
Bratsun, D., Volfson, D., Hasty, J., Tsimring, L.S.: Delay-induced stochastic oscillations in gene regulation. Proc. Natl. Acad. Sci. U.S.A. 102, 14593–14598 (2005)CrossRef
5.
Schiesser, W.E.: The Numerical Method of Lines: Integration of Partial Differential Equations. Academic Press, San Diego (1991)MATH
6.
Higham, D.J., Sardar, T.: Existence and stability of fixed points for a discretised nonlinear reaction-diffusion equation with delay. Appl. Numer. Math. 18, 155–173 (1995)CrossRefMATHMathSciNet
7.
Rey, A.D., Mackey, M.C.: Multistability and boundary layer development in a transport equation with delayed arguments. Canad. Appl. Math. Quart. 1, 61–81 (1993)MATH
8.
Jackiewicz, Z., Zubik-Kowal, B.: Spectral collocation and waveform relaxation methods for nonlinear delay partial differential equations. Appl. Numer. Math. 56, 433–443 (2006)CrossRefMATHMathSciNet
9.
Li, J., Zou, X.: Modeling spatial spread of infectious diseases with a fixed latent period in a ppatially continuous domain. Bull. Math. Biol. 71, 2048–2079 (2009)CrossRefMATHMathSciNet
10.
Smolen, P., Baxter, D.A., Byrne, J.H.: Modeling circadian oscillations with interlocking positive and negative feedback loops. J. Neurosci. 21, 6644–6656 (2001)
11.
Zubik-Kowal, B., Vandewalle, S.: Waveform relaxation for functional-differential equations. SIAM J. Sci. Comput. 21, 207–226 (1999)CrossRefMATHMathSciNet
12.
Bratsun, D., Zakharov, A.: Deterministic modeling spatio-temporal dynamics of delay-induced circadian oscillations in Neurospora crassa. In: Sanayei, A., Zelinka, I., Rössler, O.E. (eds.) ISCS 2013. Emergence, Complexity and Computation, Vol. 8, pp. 1-11. Springer, Heidelberg (2014)
Metadata
Title
Adaptive Numerical Simulations of Reaction-Diffusion Systems with Time-Delayed Feedback
Authors
Dmitry Bratsun
Andrey Zakharov
Copyright Year
2014
Publisher
Springer Berlin Heidelberg
Book
ISCS 2013: Interdisciplinary Symposium on Complex Systems

Print ISBN: 978-3-642-45437-0

Electronic ISBN: 978-3-642-45438-7

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-642-45438-7_19

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