Some Novel Real/Complex-Valued Neural Network Models

Ramamurthy, Garimella

doi:10.1007/3-540-34783-6_47

Cited by 6 publications

(4 citation statements)

References 4 publications

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“…Besides neural networks of the real parameters, recently, the introduction of complex-valued neural networks, which handle more information by using complex-valued parameters and variables, has widened applications of artificial neural net-works (Garimella, 2006), such as digital signal processing, Magnetic Resonance Imaging (MRI) reconstruction (Hirose, 2009). As shown in this section, the Lambert W function can be used to analyze dynamics of such complex-valued neural networks.…”

Section: Robust Stabilitymentioning

confidence: 99%

Analysis of Time-Delayed Neural Networks via Rightmost Eigenvalue Positions

Yi¹,

Yu²,

Kim³

et al. 2015

American Journal of Engineering and Applied Sciences

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Neural networks have been frequently used in various areas. In the implementation of the networks, time delays and uncertainty are present and known to lead to complex behaviors, which are hard to predict using classical analysis methods. In this study, stability and robust stability of neural networks considering time delays and parametric uncertainty is studied. For stability analysis, the rightmost eigenvalues (or dominant characteristic roots) are obtained by using an approach based on the Lambert W function. The Lambert W function has already been embedded in various commercial software packages (e.g., MATLAB, Maple and Mathematica). In a way similar to non-delayed systems, stability is determined from the positions of the characteristic roots in the complex plane. Conditions for oscillation and robust stability are also given. Numerical examples are provided and the results are compared to existing approaches (e.g., bifurcation method) and discussed.

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Section: Robust Stabilitymentioning

confidence: 99%

Analysis of Time-Delayed Neural Networks via Rightmost Eigenvalue Positions

Yi¹,

Yu²,

Kim³

et al. 2015

American Journal of Engineering and Applied Sciences

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“…Besides neural networks of the real parameters, recently, the introduction of complex-valued neural networks, which handle more information by using complex-valued parameters and variables, has widened applications of artificial neural networks [24], such as digital signal processing, magnetic resonance imaging (MRI) reconstruction [16]. As shown in this section, the Lambert W function can be used to analyze dynamics of such complex-valued neural networks.…”

Section: Robust Stabilitymentioning

confidence: 99%

“…Provided that the unperturbed system (20) is stable, the real structured stability radius of Eq. (23) is defined as [25] r R =inf{σ 1 (∆) : system (23) is unstable} (24) where ∆=[∆ 1 ∆ 2 ] and σ 1 (∆) denotes the largest singular value of ∆. The largest singular value, σ 1 (∆), is equal to the operator norm of ∆, which measures the size of ∆ by how much it lengthens vectors in the worst case.…”

Section: Stability Radius and Robust Stabilitymentioning

confidence: 99%

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Analysis of neural networks with time-delays using the Lambert W function

Kim

2011

Proceedings of the 2011 American Control Conference

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Neural networks have been used in various areas. In the implementation of the networks, time-delays and uncertainty are present, and induce complex behaviors. In this paper, stability and robust stability of neural networks considering time-delays and parametric uncertainty is investigated. For stability analysis, the dominant characteristic roots are obtained by using an approach based on the Lambert W function. The Lambert W function has already embedded in various commercial software packages (e.g., Matlab, Maple, and Mathematica). In a way similar to non-delay systems, stability is determined with the locations of the characteristic roots in the complex plane. Conditions for oscillation and robust stability are also given in term of the Lambert W function. Numerical examples are provided and the results are compared to existing approaches (e.g., bifurcation method) and discussed.

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