Cost Function Based on Gaussian Mixture Model for Parameter Estimation of a Chaotic Circuit with a Hidden Attractor


Seng-Kin Lao
Department of Electromechanical Engineering,
University of Macau,
Avenida Padre Tomás Pereira Taipa, Macau, P. R. China
skeltonl@umac.mo

Yasser Shekofteh
Biomedical Engineering Department,
Amirkabir University of Technology,
Tehran 15875-4413, Iran
Research Center of Intelligent Signal Processing (RCISP)
Tehran, Iran
y_shekofteh@aut.ac.ir

Sajad Jafari
Biomedical Engineering Department,
Amirkabir University of Technology,
Tehran 15875-4413, Iran
sajadjafari@aut.ac.ir

Julien Clinton Sprott
Department of Physics, University of Wisconsin-Madison,
Madison, WI 53706, USA
sprott@physics.wisc.edu

Received August 10, 2013

ABSTRACT
In this paper, we introduce a new chaotic system and its corresponding circuit. This system has a special property of having a hidden attractor. Systems with hidden attractors are newly introduced and barely investigated. Conventional methods for parameter estimation in models of these systems have some limitations caused by sensitivity to initial conditions. We use a geometry-based cost function to overcome those limitations by building a statistical model on the distribution of the real system attractor in state space. This cost function is defined by the use of a likelihood score in a Gaussian Mixture Model (GMM) which is fitted to the observed attractor generated by the real system in state space. Using that learned GMM, a similarity score can be defined by the computed likelihood score of the model time series. The results show the adequacy of the proposed cost function.

Ref: S. -K. Lao, Y. Shekofteh, S. Jafari, and J. C. Sprott, International Journal of Bifurcation and Chaos 24 1450010 (2014)

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