Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 2979-2993 |
| Number of pages | 15 |
| Journal | Nonlinear Dynamics |
| Volume | 94 |
| Issue number | 4 |
| Early online date | 18 Sep 2018 |
| DOIs | |
| Publication status | Published - 1 Dec 2018 |
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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 journal › Article
TY - JOUR
T1 - Parameter estimation for 1D PWL chaotic maps using noisy dynamics
AU - Dutta, Dhrubajyoti
AU - Basu, Rajlaxmi
AU - Banerjee, Soumitro
AU - Holmes, Violeta
AU - Mather, Peter
PY - 2018/12/1
Y1 - 2018/12/1
N2 - 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.
AB - 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.
KW - Dynamic noise
KW - Parameter estimation
KW - Reduced height map
KW - Fixed point estimates
UR - http://www.scopus.com/inward/record.url?scp=85053491614&partnerID=8YFLogxK
U2 - 10.1007/s11071-018-4538-x
DO - 10.1007/s11071-018-4538-x
M3 - Article
VL - 94
SP - 2979
EP - 2993
JO - Nonlinear Dynamics
JF - Nonlinear Dynamics
SN - 0924-090X
IS - 4
ER -