Localized numerical impulse solutions in diffuse neural networks modeled by the complex fractional Ginzburg-Landau equation

被引：45

作者：

Mvogo, Alain ^{[1
,2
,3
]}

Tambue, Antoine ^{[2
,4
,5
,6
]}

Ben-Bolie, Germain H. ^{[3
,7
]}

Kofane, Timoleon C. ^{[3
,8
]}

机构：

[1] Univ Yaounde I, Biophys Lab, Dept Phys, POB 812, Yaounde, Cameroon

[2] African Inst Math Sci, 6-8 Melrose Rd, ZA-7945 Muizenberg, South Africa

[3] Univ Yaounde I, Ctr Excellence Africain Technol Informat & Commun, Yaounde, Cameroon

[4] Univ Stellenbosch, 6-8 Melrose Rd, ZA-7945 Muizenberg, South Africa

[5] Univ Cape Town, Ctr Res Computat & Appl Mech CERECAM, ZA-7701 Rondebosch, South Africa

[6] Univ Cape Town, Dept Math & Appl Math, ZA-7701 Rondebosch, South Africa

[7] Univ Yaounde I, Dept Phys, Nucl Phys Lab, POB 812, Yaounde, Cameroon

[8] Univ Yaounde I, Dept Phys, Lab Mech, POB 812, Yaounde, Cameroon

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2016年 / 39卷

关键词：

Localized solutions; Hindmarsh-Rose neural model; Complex fractional Ginzburg-Landau equation; Riesz fractional finite-difference schemes; DYNAMICS;

D O I：

10.1016/j.cnsns.2016.03.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate localized wave solutions in a network of Hindmarsh-Rose neural model taking into account the long-range diffusive couplings. We show by a specific analytical technique that the model equations in the infrared limit (wave number k -> 0) can be governed by the complex fractional Ginzburg-Landau (CFGL) equation. According to the stiffness of the system, we propose both the semi and the linearly implicit Riesz fractional finite-difference schemes to solve efficiently the CFGL equation. The obtained fractional numerical solutions for the nerve impulse reveal localized short impulse properties. We also show the equivalence between the continuous CFGL and the discrete Hindmarsh-Rose models for relatively large network. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：396 / 410

页数：15

共 30 条

[1] Within-Burst Synchrony Changes for Coupled Elliptic Bursters [J].