A New Cost Function for Parameter Estimation of Chaotic
Systems Using Return Maps as Fingerprints
Sajad Jafari∗
Department of Biomedical Engineering,
Amirkabir University of Technology,
424 Hafez Ave., Tehran 15875–4413, Iran
sajadjafari@aut.ac.ir
Julien C. Sprott
Department of Physics,
University of Wisconsin–Madison,
Madison, WI 53706, USA
sprott@physics.wisc.edu
Viet-Thanh Pham
School of Electronics and Telecommunications,
Hanoi University of Science and Technology,
01 Dai Co Viet, Hanoi, Vietnam
pvt3010@gmail.com
S. Mohammad Reza Hashemi Golpayegani
Department of Biomedical Engineering,
Amirkabir University of Technology,
424 Hafez Ave., Tehran 15875–4413, Iran
mrhashemigolpayegani@aut.ac.ir
Amir Homayoun Jafari
Department of Medical Physics and Biomedical Engineering,
Tehran University of Medical Sciences,
Tehran 14155–6447, Iran
h jafari@tums.ac.ir
Received May 30, 2014
Estimating parameters of a model system using observed chaotic
scalar time series data is a topic of active interest. To estimate
these parameters requires a suitable similarity indicator between
the observed and model systems. Many works have considered a
similarity measure in the time domain, which has limitations because
of sensitive dependence on initial conditions. On the other hand,
there are features of chaotic systems that are not sensitive to
initial conditions
such as the topology of the strange attractor. We have used this
feature to propose a new cost function for parameter estimation of
chaotic models, and we show its efficacy for several simple chaotic
systems.
Ref: S. Jafari, J.
C. Sprott, V. T. Pham, S. M. R. H. Golpayegani, and A. H.
Jafari, International Journal of Bifurcation and Chaos 24, 1450134 (2014)
The complete paper is available in PDF
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