Transforming Analytically Intractable Dynamical Systems with a Control Parameter into a Tractable Ginzburg-Landau Equation: Few Illustrations

Authors

  • C. Kanchana College of Science, Harbin Institute of Technology, Shenzhen Graduate School, Shenzhen, Nanshan-518055, China
  • P.G. Siddheshwar Department of Mathematics, Bangalore University, Jnanabharathi Campus, Bangalore 560056, India

DOI:

https://doi.org/10.3126/nmsr.v35i1-2.29978

Keywords:

Dynamical systems, Chen, multiscale method, Ginzburg-Landau

Abstract

In the paper a means of making a simplified study of dynamical systems with a control parameter is presented. The intractable, third-order classical Lorenz system, the Lorenz-like Chen system and two topologically dissimilar fifth-order Lorenz systems are considered for illustration. Using the multi-scale method, these systems are reduced to an analytically tractable first-order Ginzburg-Landau equation (GLE) in one of the amplitudes. The analytical solution of the GLE is used to find the remaining amplitudes.

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Published

2018-12-31

How to Cite

Kanchana, C., & Siddheshwar, P. (2018). Transforming Analytically Intractable Dynamical Systems with a Control Parameter into a Tractable Ginzburg-Landau Equation: Few Illustrations. The Nepali Mathematical Sciences Report, 35(1-2), 35–44. https://doi.org/10.3126/nmsr.v35i1-2.29978

Issue

Vol. 35 No. 1-2 (2018)

Section

Articles

License

Copyright © The Nepali Mathematical Sciences Report