Torus doubling and hyperchaos in a five dimensional hysteresis circuit

Mitsubori, Kunihiko; Saito, Toshimichi

doi:10.1109/iscas.1994.409539

Cited by 13 publications

(7 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where b 0 , b 1 , b 2 , b 3 ∈ H, the signal x and noise υ were H-proper quaternion-valued white Gaussian data, and the signal-tonoise ratio (SNR) was 10 dB. Figure 6a illustrates that when estimating the strictly linear MA system in (32), FC-QLMS, WL-QLMS, SC-QLMS, and SL-QLMS behaved identically, while the FC-QLMS and SC-QLMS with an adaptive step-size (31), which are referred to as the adaptive FC-QLMS and adaptive SC-QLMS, exhibited faster convergence. Figure 6b shows that when estimating the widely linear MA system in (33), the FC-QLMS and the WL-QLMS behaved identically, and had a much smaller steady-state NMSE than the SL-QLMS, while the adaptive FC-QLMS converged fastest.…”

Section: Qlmsmentioning

confidence: 99%

See 1 more Smart Citation

Cost-effective quaternion minimum mean square error estimation: From widely linear to four-channel processing

2017

View full text Add to dashboard Cite

Section: Qlmsmentioning

confidence: 99%

“…The QNGD algorithms were employed in a one-step ahead prediction of the 4-D Saito's chaotic circuit data, which is governed by four state variables x 1 , y 1 , x 2 , y 2 and five parameters, as [31]    ∂x1 ∂τ ∂y1 ∂τ…”

Section: Qngdmentioning

confidence: 99%

Cost-effective quaternion minimum mean square error estimation: From widely linear to four-channel processing

2017

View full text Add to dashboard Cite

“…The three quaternion-valued processes 5 The QNGD could also be readily extended to incorporate the semi-widely linear model [22], however this is beyond the scope of this paper. considered were the synthetic linear autoregressive (AR) (4) process [13] with a varying degree of circularity, the noncircular chaotic 4-D Saito signal [39], and the real-world 3-D wind field.…”

Section: Simulationsmentioning

confidence: 99%

“…The four state variables and five parameters that govern the noncircular Saito's chaotic process are given by [39] …”

Section: B 4-d Saito's Chaotic Circuitmentioning

confidence: 99%

“…where τ is the time constant of the chaotic circuit and h(z) is the normalized hysteresis value given by [39] h The parameters z, ρ 1 , and ρ 2 are given as z = x 1 + x 2 , ρ 1 = (β 1 /1 − β 1 ), and ρ 2 = (β 2 /1 − β 2 ). The Saito chaotic signal was initialized with the following parameters: η = 1.3, α 1 = 7.5, α 2 = 15, β 1 = 0.16, and β 2 = 0.097, and is noncircular, as shown dimensionwise in Fig.…”

Section: B 4-d Saito's Chaotic Circuitmentioning

confidence: 99%

See 1 more Smart Citation

Quaternion-Valued Nonlinear Adaptive Filtering

Ujang

Took

Mandic

2011

IEEE Trans. Neural Netw.

184

View full text Add to dashboard Cite

Abstract-A class of nonlinear quaternion-valued adaptive filtering algorithms is proposed based on locally analytic nonlinear activation functions. To circumvent the stringent standard analyticity conditions which are prohibitive to the development of nonlinear adaptive quaternion-valued estimation models, we use the fact that stochastic gradient learning algorithms require only local analyticity at the operating point in the estimation space. It is shown that the quaternion-valued exponential function is locally analytic, and, since local analyticity extends to polynomials, products, and ratios, we show that a class of transcendental nonlinear functions can serve as activation functions in nonlinear and neural adaptive models. This provides a unifying framework for the derivation of gradient-based learning algorithms in the quaternion domain, and the derived algorithms are shown to have the same generic form as their real-and complex-valued counterparts. To make such models second-order optimal for the generality of quaternion signals (both circular and noncircular), we use recent developments in augmented quaternion statistics to introduce widely linear versions of the proposed nonlinear adaptive quaternion valued filters. This allows full exploitation of second-order information in the data, contained both in the covariance and pseudocovariances to cater rigorously for second-order noncircularity (improperness), and the corresponding power mismatch in the signal components. Simulations over a range of circular and noncircular synthetic processes and a real world 3-D noncircular wind signal support the approach.Index Terms-Augmented quaternion statistics, H-circularity, nonlinear adaptive filtering, quaternion least mean square, widely linear modeling, widely linear quaternion least mean square, wind prediction.

show abstract

Quaternion Extreme Learning Machine

Zhang

2017

Proceedings in Adaptation, Learning and Optimization

View full text Add to dashboard Cite

Torus doubling and hyperchaos in a five dimensional hysteresis circuit

Cited by 13 publications

References 4 publications

Cost-effective quaternion minimum mean square error estimation: From widely linear to four-channel processing

Cost-effective quaternion minimum mean square error estimation: From widely linear to four-channel processing

Quaternion-Valued Nonlinear Adaptive Filtering

Quaternion Extreme Learning Machine

Contact Info

Product

Resources

About