Frequency domain approach to the critical step size of discrete-time recurrent neural networks

被引：4

作者：

Hou, Hu-Shuang ^{[1
]}

Luo, Cheng ^{[2
]}

Zhang, Hua ^{[1
]}

Wu, Guo-Cheng ^{[3
]}

机构：

[1] Chongqing Univ Technol, Sch Sci, Chongqing 400054, Peoples R China

[2] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

[3] Neijiang Normal Univ, Coll Math & Informat Sci, Data Recovery Key Lab Sichuan Prov, Neijiang 641100, Sichuan, Peoples R China

来源：

NONLINEAR DYNAMICS | 2023年 / 111卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Discrete-time neural networks; Hopf bifurcation; Frequency domain approach; Harmonic balance method; HOPF-BIFURCATION ANALYSIS; STABILITY; MODEL;

D O I：

10.1007/s11071-023-08278-0

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

It is usually essential to reveal the relationship between continuous-time systems and discrete-time ones. First, a discrete-time recurrent neural network is presented by the Euler scheme in this paper. Then, the time step size is set to a bifurcation parameter and frequency domain approach is adopted for Hopf bifurcation analysis. Moreover, the periodic solutions are obtained by the harmonic balance method; then the stability conditions are presented. The critical step size is determined with which the discrete-time recurrent neural network can inherit the stable state of the continuous-time one. Finally, one numerical example of the discrete-time recurrent neural network is given to support the theoretical analysis.

引用

页码：8467 / 8476

页数：10

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