PATTERN FORMATION IN REACTION-DIFFUSION NEURAL NETWORKS WITH LEAKAGE DELAY

被引：7

作者：

Lin, Jiazhe ^{[1
]}

Xu, Rui ^{[2
]}

Tian, Xiaohong ^{[2
]}

机构：

[1] Army Engn Univ, Inst Appl Math, Shijiazhuang 050003, Hebei, Peoples R China

[2] Shanxi Univ, Complex Syst Res Ctr, Taiyuan 030006, Shanxi, Peoples R China

来源：

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2019年 / 9卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Pattern formation; reaction-diffusion; leakage delay; neural network; amplitude equation; HOPF-BIFURCATION ANALYSIS; ASSOCIATIVE MEMORY; 2-NEURON NETWORK; TIME-DELAY; DYNAMICS; MODEL;

D O I：

10.11948/20190001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Due to the heterogeneity of the electromagnetic field in neural networks, the diffusion phenomenon of electrons exists inevitably. In this paper, we investigate pattern formation in a reaction-diffusion neural network with leakage delay. The existence of Hopf bifurcation, as well as the necessary and sufficient conditions for Turing instability, are studied by analyzing the corresponding characteristic equation. Based on the multiple-scale analysis, amplitude equations of the model are derived, which determine the selection and competition of Turing patterns. Numerical simulations are carried out to show the possible patterns and how these patterns evolve. In some cases, the stability performance of Turing patterns is weakened by leakage delay and synaptic transmission delay.

引用

页码：2224 / 2244

页数：21

共 31 条

[1] Analysis and design of associative memories based on recurrent neural network with discontinuous activation functions [J].

Bao, Gang ;

Zeng, Zhigang .

NEUROCOMPUTING, 2012, 77 (01) :101-107

[2] Turing patterns in cellular neural networks [J].

Chua, LO ;

Goras, L .

INTERNATIONAL JOURNAL OF ELECTRONICS, 1995, 79 (06) :719-736

[3]

Deb T, 2018, MATER TODAY-PROC, V5, P2222

[4] Finite-difference schemes for reaction-diffusion equations modeling predator-prey interactions in MATLAB [J].

Garvie, Marcus R. .

BULLETIN OF MATHEMATICAL BIOLOGY, 2007, 69 (03) :931-956

[5] Leakage delays in BAM [J].

Gopalsamy, K. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 325 (02) :1117-1132

[6]

Gopalsamy K., 2013, Stability and Oscillations in Delay Differential Equations of Population Dynamics, V74

[7] Turing Patterns of a Lotka-Volterra Competitive System with Nonlocal Delay [J].

Han, Bang-Sheng ;

Wang, Zhi-Cheng .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2018, 28 (07)

[8] Impact of leakage delay on bifurcation in high-order fractional BAM neural networks [J].

Huang, Chengdai ;

Cao, Jinde .

NEURAL NETWORKS, 2018, 98 :223-235

[9] New bifurcation results for fractional BAM neural network with leakage delay [J].

Huang, Chengdai ;

Meng, Yijie ;

Cao, Jinde ;

Alsaedi, Ahmed ;

Alsaadi, Fuad E. .

CHAOS SOLITONS & FRACTALS, 2017, 100 :31-44

[10] Hopf bifurcation analysis for a two-neuron network with four delays [J].

Huang, Chuangxia ;

Huang, Lihong ;

Feng, Hanfeng ;

Nai, Mingyong ;

He, Yigang .

CHAOS SOLITONS & FRACTALS, 2007, 34 (03) :795-812

← 1 2 3 4 →