一类比例时滞随机神经网络的均方指数同步及应用

摘要/Abstract

图/表 8

参考文献 27

Metrics

摘要：

以一类比例时滞惯性随机神经网络作为驱动-响应系统, 通过降阶法, 采用状态反馈控制器, 利用 Itô 积分, 通过构造新颖的 Lyapunov 泛函和利用微积分性质分析所研究系统的均方指数同步, 得到所研究系统均方指数同步的判定准则. 最后, 通过数值算例及仿真验证所得判定准则的准确性, 并给出所研究的指数同步在图像加密和解密中的应用．

关键词: 随机神经网络, 惯性项, 均方指数同步, 比例时滞, 图像加密和解密

Abstract:

A class of proportional delay inertial stochastic neural networks is used as the driving-response systems. The mean square exponential synchronization of the studied system is analyzed by reducing the order method, adopting a state feedback controller, utilizing Itô integral, constructing a novel Lyapunov functional, and utilizing the properties of calculus. The criteria for determining the mean square exponential synchronization of the studied system are obtained. Finally, the accuracy of the judgment criteria obtained is verified through a numerical example and simulations, and the application of the studied exponential synchronization in image encryption and decryption is presented.

Key words: stochastic neural networks, inertia term, mean square exponential synchronization, proportional delay, encryption and decryption of image

中图分类号:

O175.13

任红越, 周立群. 一类比例时滞随机神经网络的均方指数同步及应用[J]. 数学物理学报, 2025, 45(3): 888-901.

Ren Hongyue, Zhou Liqun. Mean Square Exponential Synchronization of a Class of Proportional Delay Stochastic Neural Networks and Its Application[J]. Acta mathematica scientia,Series A, 2025, 45(3): 888-901.

图1

图2

图3

图4

(a) 图像 $A$ 的原图; (b) 驱动系统加密后的图像 $A^{\prime}$ ; (c) 响应系统解密后的图像; (a) 的直方图; (e) (b) 的直方图; (f) (c) 的直方图"

图4

表1

图5

(a) 同步误差 $10^{-5}$ ; (b) 同步误差 $10^{-4}$ ; (c) 同步误差 $10^{-3}$ "

图5

表2

图6

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