Parameter estimation for 1D PWL chaotic maps using noisy dynamics

Dhrubajyoti Dutta, Rajlaxmi Basu, Soumitro Banerjee, Violeta Holmes, Peter Mather

Research output: Contribution to journalArticle

Abstract

Many physical situations involve chaotic systems implemented in hardware. Among them one-dimensional piecewise linear maps are popular candidates for such applications because of their property of generating robust chaos. In physical implementations, the control parameter of these maps may deviate from its ideal value due to hardware imprecision. Since the dynamics of a chaotic map is completely defined by its control parameter, one needs to know the value of the parameter in a hardware realisation. In this paper, we show that it is possible to determine the parameter, through the realisation of the unstable fixed point of the map, by utilising noise that is always present in the system. We present this in the form of an algorithm and demonstrate its efficacy through simulated results. We also determine the bounds on the signal-to-noise ratio required for successful parameter estimation. The proposed approach is expected to be beneficial to the existing noise reduction techniques and time series recovery algorithms that require a reasonably accurate knowledge of the map.
Original languageEnglish
Pages (from-to)2979-2993
Number of pages15
JournalNonlinear Dynamics
Volume94
Issue number4
Early online date18 Sep 2018
DOIs
Publication statusPublished - 1 Dec 2018

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Chaotic Map
Parameter estimation
Parameter Estimation
Hardware
Control Parameter
Piecewise Linear Map
Imprecision
Noise Reduction
Chaotic System
Efficacy
Chaos
Recovery
Time series
Unstable
Fixed point
Chaotic systems
Noise abatement
Chaos theory
Signal to noise ratio
Demonstrate

Cite this

Dutta, Dhrubajyoti ; Basu, Rajlaxmi ; Banerjee, Soumitro ; Holmes, Violeta ; Mather, Peter. / Parameter estimation for 1D PWL chaotic maps using noisy dynamics. In: Nonlinear Dynamics. 2018 ; Vol. 94, No. 4. pp. 2979-2993.
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Parameter estimation for 1D PWL chaotic maps using noisy dynamics. / Dutta, Dhrubajyoti; Basu, Rajlaxmi; Banerjee, Soumitro; Holmes, Violeta; Mather, Peter.

In: Nonlinear Dynamics, Vol. 94, No. 4, 01.12.2018, p. 2979-2993.

Research output: Contribution to journalArticle

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