From Davidenko Method to Zhang Dynamics for Nonlinear Equation Systems Solving

The solving of nonlinear equation systems (e.g., complex transcendental dispersion equation systems in waveguide systems) is a fundamental topic in science and engineering. Davidenko method has been used by electromagnetism researchers to solve time-invariant nonlinear equation systems (e.g., the af...

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Bibliographic Details
Published in:IEEE transactions on systems, man, and cybernetics. Systems man, and cybernetics. Systems, 2017-11, Vol.47 (11), p.2817-2830
Main Authors: Zhang, Yunong, Zhang, Yinyan, Chen, Dechao, Xiao, Zhengli, Yan, Xiaogang
Format: Article
Language:English
Subjects:
Block diagrams
Comparison
Convergence
Davidenko method
Dispersion
Economic models
Electromagnetics
Electromagnetism
Invariants
Mathematical model
Newton method
Nonlinear equations
Nonlinear systems
On-line systems
Researchers
System effectiveness
time-invariant nonlinear equation systems
time-varying nonlinear equation systems
Time-varying systems
Zhang dynamics (ZD)
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Summary:The solving of nonlinear equation systems (e.g., complex transcendental dispersion equation systems in waveguide systems) is a fundamental topic in science and engineering. Davidenko method has been used by electromagnetism researchers to solve time-invariant nonlinear equation systems (e.g., the aforementioned transcendental dispersion equation systems). Meanwhile, Zhang dynamics (ZD), which is a special class of neural dynamics, has been substantiated as an effective and accurate method for solving nonlinear equation systems, particularly time-varying nonlinear equation systems. In this paper, Davidenko method is compared with ZD in terms of efficiency and accuracy in solving time-invariant and time-varying nonlinear equation systems. Results reveal that ZD is a more competent approach than Davidenko method. Moreover, discrete-time ZD models, corresponding block diagrams, and circuit schematics are presented to facilitate the convenient implementation of ZD by researchers and engineers for solving time-invariant and time-varying nonlinear equation systems online. The theoretical analysis and results on Davidenko method, ZD, and discrete-time ZD models are also discussed in relation to solving time-varying nonlinear equation systems.
ISSN:2168-2216
2168-2232
DOI:10.1109/TSMC.2016.2523917