Complex nonlinear dynamics in subdiffusive activator-inhibitor systems

被引：28

作者：

Datsko, B. ^{[1
]}

Gafiychuk, V. ^{[2
,3
]}

机构：

[1] Natl Acad Sci Ukraine, Inst Appl Problems Mech & Math, UA-79060 Lvov, Ukraine

[2] SGT Inc, Greenbelt, MD 20770 USA

[3] NASA, Ames Res Ctr, Moffett Field, CA 94035 USA

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2012年 / 17卷 / 04期

关键词：

Reaction-diffusion system; Fractional differential equations; Homogeneous oscillations; Dissipative structures; PATTERN-FORMATION; DIFFUSION; EQUATION; WAVES;

D O I：

10.1016/j.cnsns.2011.08.037

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article we analyze the linear stability of nonlinear time-fractional reaction-diffusion systems. As an example, the reaction-subdiffusion model with cubic nonlinearity is considered. By linear stability analysis and computer simulation, it was shown that fractional derivative orders can change substantially an eigenvalue spectrum and significantly enrich nonlinear system dynamics. A overall picture of nonlinear solutions in subdiffusive reaction-diffusion systems is presented. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：1673 / 1680

页数：8

共 34 条

[1]

ABAD S, 2010, PHYS REV E, V81

[2]

Agrawal O, 2007, ADV FRACTIONAL CALCU

[3] Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions [J].

Ahmad, Bashir ;

Nieto, Juan J. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2009, 58 (09) :1838-1843

[4]

[Anonymous], 2006, THEORY APPL FRACTION

[5]

[Anonymous], 1994, Autosolitons

[6]

[Anonymous], 1999, FRACTIONAL DIFFERENT

[7]

[Anonymous], 1997, SELF ORG NONEQUILIBR

[8]

BALACHANDRAN K, 2010, NONLINEAR ANAL-THEOR, V72

[9] PATTERN-FORMATION OUTSIDE OF EQUILIBRIUM [J].

CROSS, MC ;

HOHENBERG, PC .

REVIEWS OF MODERN PHYSICS, 1993, 65 (03) :851-1112

[10] Mathematical modeling of time fractional reaction-diffusion systems [J].

Gafiychuk, V. ;

Datsko, B. ;

Meleshko, V. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 220 (1-2) :215-225

← 1 2 3 4 →