Summary

Proceedings of the 2013 International Symposium on Nonlinear Theory and its Applications

2013

Session Number:A4L-C

Session:

Number:158

Controlling Method to Avoid Bifurcations of Periodic Points Using Maximum Lyapunov Exponent

Ken'ichi Fujimoto,  Tomohiro Otsu,  Tetsuya Yoshinaga,  Tetsushi Ueta,  Hiroyuki Kitajima,  Kazuyuki Aihara,  

pp.158-161

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.2.158

PDF download (886KB)

Summary:
This paper provides a novel controlling method to avoid improper bifurcations of stable fixed and periodic points using the maximum Lyapunov exponent. The Lyapunov exponents that can be calculated from the sequence of the points characterize the topological properties of a stable fixed or periodic point if it is the limit of the sequence. Our main ideas are observing the maximum Lyapunov exponent to predict a bifurcation caused by the change of any parameter value, and controlling any adjustable system-parameter value so that the bifurcation never appears. The proposed method can be led from an optimization problem on the maximum Lyapunov exponent. We presented not only its mathematical derivation but also the results of numerical experiments on avoiding bifurcations to demonstrate the validity of the proposed method.

References:

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