Mittag-Leffler stability and generalized Mittag-Leffler stability of fractional-order gene regulatory networks

被引：103

作者：

Ren, Fengli ^{[1
]}

Cao, Feng ^{[1
]}

Cao, Jinde ^{[2
,3
]}

机构：

[1] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 210016, Peoples R China

[2] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China

[3] King Abdulaziz Univ, Dept Math, Fac Sci, Jeddah 21589, Saudi Arabia

来源：

NEUROCOMPUTING | 2015年 / 160卷

基金：

中国国家自然科学基金;

关键词：

Fractional-order; Mittag-Leffler stability; Generalized Mittag-Leffler stability; Gene regulatory networks; NEURAL-NETWORKS; ROBUST STABILITY; SYNCHRONIZATION; SYSTEM;

D O I：

10.1016/j.neucom.2015.02.049

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Gene regulatory networks have attracted much attention, and the networks with integer-order have been well studied. Fractional-order gene regulatory networks have been shown that it is more suitable to model gene regulation mechanism, but has rarely been researched. In this paper, a class of fractional-order gene regulatory networks is studied. Some criteria on the Mittag-Leffler stability and generalized Mittag-Leffler stability are established by using the fractional Lyapunov method for these networks. The existence of the equilibrium point is also considered. One illustrative example is provided to show the effectives of the obtained results. (C) 2015 Published by Elsevier B.V.

引用

页码：185 / 190

页数：6

共 26 条

[11] Chaos and hyperchaos in fractional-order cellular neural networks [J].

Huang, Xia ;

Zhao, Zhao ;

Wang, Zhen ;

Li, Yuxia .

NEUROCOMPUTING, 2012, 94 :13-21

[12] Robust stability analysis of gene-protein regulatory networks with cyclic activation-repression interconnections [J].

Kim, Tae-Hyoung ;

Hori, Yutaka ;

Hara, Shinji .

SYSTEMS & CONTROL LETTERS, 2011, 60 (06) :373-382

[13] Synchronization of coupled nonidentical genetic oscillators [J].

Li, CG ;

Chen, LJN ;

Aihara, K .

PHYSICAL BIOLOGY, 2006, 3 (01) :37-44

[14] Stability of genetic networks with SUM regulatory logic: Lur'e system and LMI approach [J].

Li, Chunguang ;

Chen, Luonan ;

Aihara, Kazuyuki .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 2006, 53 (11) :2451-2458

[15] Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability [J].

Li, Yan ;

Chen, YangQuan ;

Podlubny, Igor .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 59 (05) :1810-1821

[16] Mittag-Leffler stability of fractional order nonlinear dynamic systems [J].

Li, Yan ;

Chen, YangQuan ;

Podlubny, Igor .

AUTOMATICA, 2009, 45 (08) :1965-1969

[17] Completely monotonic functions [J].

Miller, KS ;

Samko, SG .

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2001, 12 (04) :389-402

[18]

Momani S., 2004, Int. J. Math. Math. Sc, V47, P2503, DOI DOI 10.1155/S0161171204312366

[19]

Podlubny Igor, 1998, Fractional differential equationsM

[20] Asymptotic and robust stability of genetic regulatory networks with time-varying delays [J].

Ren, Fengi ;

Cao, Jinde .

NEUROCOMPUTING, 2008, 71 (4-6) :834-842

← 1 2 3 →