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A New Mechanical Algorithm for Calculating the Amplitude Equation of the Reaction-Diffusion Systems

A New Mechanical Algorithm for Calculating the Amplitude Equation of the Reaction-Diffusion Systems

Houye Liu, Weiming Wang
Copyright: © 2012 |Volume: 3 |Issue: 4 |Pages: 8
ISSN: 1947-3133|EISSN: 1947-3141|EISBN13: 9781466611245|DOI: 10.4018/ijcmam.2012100103
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MLA

Liu, Houye, and Weiming Wang. "A New Mechanical Algorithm for Calculating the Amplitude Equation of the Reaction-Diffusion Systems." IJCMAM vol.3, no.4 2012: pp.21-28. http://doi.org/10.4018/ijcmam.2012100103

APA

Liu, H. & Wang, W. (2012). A New Mechanical Algorithm for Calculating the Amplitude Equation of the Reaction-Diffusion Systems. International Journal of Computational Models and Algorithms in Medicine (IJCMAM), 3(4), 21-28. http://doi.org/10.4018/ijcmam.2012100103

Chicago

Liu, Houye, and Weiming Wang. "A New Mechanical Algorithm for Calculating the Amplitude Equation of the Reaction-Diffusion Systems," International Journal of Computational Models and Algorithms in Medicine (IJCMAM) 3, no.4: 21-28. http://doi.org/10.4018/ijcmam.2012100103

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Abstract

Amplitude equation may be used to study pattern formatio. In this article, the authors establish a new mechanical algorithm AE_Hopf for calculating the amplitude equation near Hopf bifurcation based on the method of normal form approach in Maple. The normal form approach needs a large number of variables and intricate calculations. As a result, deriving the amplitude equation from diffusion-reaction is a difficult task. Making use of our mechanical algorithm, we derived the amplitude equations from several biology and physics models. The results indicate that the algorithm is easy to apply and effective. This algorithm may be useful for learning the dynamics of pattern formation of reaction-diffusion systems in future studies.

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