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
[email protected]

Julien C. Sprott
Department of Physics,
University of Wisconsin–Madison,
Madison, WI 53706, USA
[email protected]

Viet-Thanh Pham
School of Electronics and Telecommunications,
Hanoi University of Science and Technology,
01 Dai Co Viet, Hanoi, Vietnam
[email protected]

S. Mohammad Reza Hashemi Golpayegani
Department of Biomedical Engineering,
Amirkabir University of Technology,
424 Hafez Ave., Tehran 15875–4413, Iran
[email protected]

Amir Homayoun Jafari
Department of Medical Physics and Biomedical Engineering,
Tehran University of Medical Sciences,
Tehran 14155–6447, Iran
h [email protected]

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 format.

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