Existence and Stability of Periodic Solution to Delayed Nonlinear Differential Equations

被引:2
作者
Gu, Xiang [1 ]
Wang, Huicheng [1 ]
Wong, P. J. Y. [2 ]
Xia, Yonghui [1 ]
机构
[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China
[2] Nanyang Technol Univ, Sch Elect & Elect Engn, Singapore 639798, Singapore
基金
中国国家自然科学基金;
关键词
GLOBAL ATTRACTIVITY; COMPETITION; MODEL; GROWTH; SYSTEM;
D O I
10.1155/2014/156948
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The main purpose of this paper is to study the periodicity and global asymptotic stability of a generalized Lotka-Volterra's competition system with delays. Some sufficient conditions are established for the existence and stability of periodic solution of such nonlinear differential equations. The approaches are based on Mawhin's coincidence degree theory, matrix spectral theory, and Lyapunov functional.
引用
收藏
页数:12
相关论文
共 23 条
[1]  
[Anonymous], 1979, NONNEGATIVE MATRICES
[2]  
[Anonymous], 1977, COINCIDENCE DEGREE N, DOI DOI 10.1007/BFB0089537
[3]   COMPETITION BETWEEN SPECIES - THEORETICAL MODELS AND EXPERIMENTAL TESTS [J].
AYALA, FJ ;
GILPIN, ME ;
EHRENFELD, JG .
THEORETICAL POPULATION BIOLOGY, 1973, 4 (03) :331-356
[4]  
Barbalat I., 1959, Rev. Math. Pures Appl., V4, P267
[5]   Average conditions for permanence and extinction in nonautonomous Gilpin-Ayala competition model [J].
Chen, Fengde .
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2006, 7 (04) :895-915
[6]   DISCRETE DELAY, DISTRIBUTED DELAY AND STABILITY SWITCHES [J].
COOKE, KL ;
GROSSMAN, Z .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1982, 86 (02) :592-627
[7]   Dynamic of a non-autonomous predator-prey system with infinite delay and diffusionl [J].
Ding, Wei ;
Han, Maoan .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (05) :1335-1350
[8]  
Djellit I, 2013, J APPL ANAL COMPUT, V3, P11
[9]   Existence and global attractivity of positive periodic solutions of periodic n-species Lotka-Volterra competition systems with several deviating arguments [J].
Fan, M ;
Wang, K ;
Jian, DQ .
MATHEMATICAL BIOSCIENCES, 1999, 160 (01) :47-61
[10]   GLOBAL MODELS OF GROWTH AND COMPETITION [J].
GILPIN, ME ;
AYALA, FJ .
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1973, 70 (12) :3590-3593