NDLI: Performance tests for a Micro-Integrator algorithm which reduces the numerical butterfly effect in time evolving nonlinear systems

Content Provider	IEEE Xplore Digital Library
Author	Jemegbe, J.M. Pieper, R.J.
Copyright Year	2012
Description	Author affiliation: Department of Electrical Engineering, University of Texas at Tyler, Tyler, Texas (Jemegbe, J.M.; Pieper, R.J.)
Abstract	In computing solutions to chaotic systems, slight deviations in step size could lead to completely diverging trajectories as the system's time series progresses. This is called the numerical butterfly effect. Smaller step sizes produce arrays closer to the desired continuous time solution, but they require more sampling points and as a result more memory. The Micro-Integrator produces results with a high level of accuracy while using only a fraction of the amount of memory required by conventional numerical integration methods. The reduction in memory requirements by the Micro-Integrator was quantified by introducing a performance factor ‘η’ that was mathematically equal to the ratio of the amount of memory required for computing without the Micro-Integrator to that required for computing with it. Recorded values of the performance factor from the tests ranged from 5 to 10,000; most of them were above 1,000. The performance factor was also found to depend on the type of chaotic system, the numerical method, and the time window for computation. Less computationally efficient numerical methods led to higher performance factors.
Starting Page	237
Ending Page	242
File Size	605803
Page Count	6
File Format	PDF
ISBN	9781457714924
ISSN	00942898
e-ISBN	9781457714931
DOI	10.1109/SSST.2012.6195149
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-03-11
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Equations Chaotic communication Memory management Mathematical model Encryption Trajectory Chaotic Systems Butterfly Effect
Content Type	Text
Resource Type	Article

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