Convergence analysis of the nontrivial stationary solution of the memristor-based neural networks with reaction-diffusion terms

被引:0
作者
Wang, Helin [1 ]
Jiang, Xinrui [1 ]
Qin, Sitian [1 ]
Zhang, Wei [2 ]
Feng, Yuming [2 ]
机构
[1] Harbin Inst Technol, Dept Math, Weihai, Peoples R China
[2] Chongqing Three Gorges Univ, Sch Comp Sci & Engn, Chongqing, Peoples R China
来源
2023 15TH INTERNATIONAL CONFERENCE ON ADVANCED COMPUTATIONAL INTELLIGENCE, ICACI | 2023年
关键词
memristor-based; reaction-diffusion terms; nontrivial solution; Leary-Schauder alternative theorem; TO-STATE STABILITY;
D O I
10.1109/ICACI58115.2023.10146155
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
This paper considers the convergence and existence problem for the nontivial stationary solution of a memristor-based neural network with reaction-diffusion(MNNs). We address the existence of the nontrivial stationary solution by investigating a compact operator whose fixed point is exactly the stationary solution through the Leary-Schauder theorem. Then, under some mild conditions, a lyapounov function is proposed to prove the convergence of the stationary solution. Numerial examples are provided to support the effectiveness of the conclusions.
引用
收藏
页数:8
相关论文
共 20 条
[1]   MEMRISTOR - MISSING CIRCUIT ELEMENT [J].
CHUA, LO .
IEEE TRANSACTIONS ON CIRCUIT THEORY, 1971, CT18 (05) :507-+
[2]  
Evans L. C., 2010, Partial Differential Equations, V19
[3]  
Gilbarg D., 1983, ELLIPTIC PARTIAL DIF
[4]   SOME MATHEMATICAL PROBLEMS FROM NEUROBIOLOGY [J].
HASTINGS, SP .
AMERICAN MATHEMATICAL MONTHLY, 1975, 82 (09) :881-895
[5]   Effects of external stimulations on transition behaviors in neural network with time-delay [J].
Huang, Shoufang ;
Zhang, Jiqian ;
Hu, Chin-Kun .
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2019, 536
[6]   Robust Exponential Synchronization for Memristor Neural Networks With Nonidentical Characteristics by Pinning Control [J].
Li, Yueheng ;
Luo, Biao ;
Liu, Derong ;
Yang, Yin ;
Yang, Zhanyu .
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS, 2021, 51 (03) :1966-1980
[7]  
Marino Badiale, 2010, SEMILINEAR ELLIPTIC, V2011
[8]   Exponential stability of periodic solution for a memristor-based inertial neural network with time delays [J].
Qin, Sitian ;
Gu, Liyuan ;
Pan, Xinyu .
NEURAL COMPUTING & APPLICATIONS, 2020, 32 (08) :3265-3281
[9]   Stability analysis of nontrivial stationary solution and constant equilibrium point of reaction-diffusion neural networks with time delays under Dirichlet zero boundary value [J].
Rao, Ruofeng ;
Huang, Jialin ;
Li, Xiaodi .
NEUROCOMPUTING, 2021, 445 :105-120
[10]   Stability and Robust Stability of Stochastic Reaction-Diffusion Neural Networks With Infinite Discrete and Distributed Delays [J].
Sheng, Yin ;
Zhang, Hao ;
Zeng, Zhigang .
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS, 2020, 50 (05) :1721-1732