数学物理学报(英文版) ›› 1994, Vol. 14 ›› Issue (1): 19-23.

• 论文 • 上一篇    下一篇

STABLEP OSITIVE PERIODIC SOLUTION OF TIME DEPENDENT LOTKA-VOLTERRA PERIODIC MUTUALISTIC SYSTEM STABLEP OSITIVE PERIODIC SOLUTION OF TIME DEPENDENT LOTKA-VOLTERRA PERIODIC MUTUALISTIC SYSTEM

崔景安1, 陈兰荪2   

  1. 1. Dept. of Math., Xinjiang Univ. Urmuqi 830046, China;
    2. Inst. of Math., Academia Sinica, Beijing 100080, China
  • 收稿日期:1991-07-15 出版日期:1994-03-25 发布日期:1994-03-25
  • 基金资助:
    This work is supported by the National Science Foundation of China.

STABLEP OSITIVE PERIODIC SOLUTION OF TIME DEPENDENT LOTKA-VOLTERRA PERIODIC MUTUALISTIC SYSTEM STABLEP OSITIVE PERIODIC SOLUTION OF TIME DEPENDENT LOTKA-VOLTERRA PERIODIC MUTUALISTIC SYSTEM

Cui Jing'an1, Chen Lansun2   

  1. 1. Dept. of Math., Xinjiang Univ. Urmuqi 830046, China;
    2. Inst. of Math., Academia Sinica, Beijing 100080, China
  • Received:1991-07-15 Online:1994-03-25 Published:1994-03-25
  • Supported by:
    This work is supported by the National Science Foundation of China.

PDF (PC)

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摘要： The time dependent Lotka-Volterra mutualistic system
ẋi=xi(ri(t)+∑j=1naij(t)xj),(i=1,…,n) be considered under the assumption that ri(t) and aij (t) are ω-periodic functions. A set of easily verifiable sufficient conditions are given which gurantee the global asymptotic stability of positive ω-perodic solution of system (1). When ri(t), aij(t) are constants, the conditions are coincident with the necessary and sufficient condition that the positive equilibrium (if there exists) is global asymptotic stable.

Abstract: The time dependent Lotka-Volterra mutualistic system
ẋi=xi(ri(t)+∑j=1naij(t)xj),(i=1,…,n) be considered under the assumption that ri(t) and aij (t) are ω-periodic functions. A set of easily verifiable sufficient conditions are given which gurantee the global asymptotic stability of positive ω-perodic solution of system (1). When ri(t), aij(t) are constants, the conditions are coincident with the necessary and sufficient condition that the positive equilibrium (if there exists) is global asymptotic stable.

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