NDLI: Quadratic neural unit for adaptive prediction of transitions among local attractors of Lorenz system

Content Provider	IEEE Xplore Digital Library
Author	Bukovsky, I. Anderle, F. Smetana, L.
Copyright Year	2008
Description	Author affiliation: Dept. of Instrum. & Control Eng., Czech Tech. Univ. in Prague, Prague (Bukovsky, I.; Anderle, F.; Smetana, L.)
Abstract	The goal of the paper is to demonstrate an adaptive prediction of trajectory transitions between local attractors of deterministic chaotic systems using low-dimensional dynamic quadratic neural unit with periodically forced neural inputs. The forthcoming transitions of higher dimensional chaotic systems are predicted by a low dimensional discrete dynamic neural unit implemented as a special adaptive forced oscillator. The real-time sample-by-sample evaluation of complex system behavior is based on monitoring of parameters of an adaptive model during its adaptation. The behavior of chaotic systems in the state-space is adaptively transformed to system behavior in an approximated parameter-space using special higher order nonlinear neural unit forced with periodical inputs. Added forcing inputs naturally allow a low dimensional dynamic neural unit to better approximate higher dimensional behavior; the forcing neural inputs are initially configured upon analysis of frequency spectra of the evaluated time series. It is demonstrated that monitoring of system parameters during adaptation of a dynamic neural architecture can reveal important attributes of complex behavior in real time, and should be considered as a novel methodology for early detection of transients between local attractors of higher dimensional chaotic systems (transient chaos) by lower dimensional adaptive evaluating systems, i.e. a neural unit with forcing inputs. The stable learning technique combining consequent adaptation of the static and dynamic neural unit is discussed. Results are shown on the application of monitoring and detection of significant transitions among local basins of attraction in deterministic chaotic time series generated first by Lorenz system in a chaotic mode and second by a high dimensional complex nonlinear dynamic system.
Starting Page	147
Ending Page	152
File Size	231307
Page Count	6
File Format	PDF
ISBN	9781424425020
DOI	10.1109/ICAL.2008.4636136
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-09-01
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Chaos forced nonlinear dynamic oscillator Adaptive systems chaos Dynamics higher order nonlinear neural unit Nonlinear dynamical systems Trajectory Approximation methods adaptive evaluation Monitoring inter-attractor transition
Content Type	Text
Resource Type	Article

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