摘要
研究了时变Ｌｏｇｉｓｔｉｃ方程ｄｘｄｔ＝ｒ（ｔ）ｘ（１－ｘＫ（ｔ））解的一些渐近性态，我们记Ｋ＝ｓｕｐｔ∈ＲＫ（ｔ），ｋ＝ｉｎｆｔ∈ＲＫ（ｔ），若０＜ｋ′＜ｋＫ＜Ｋ′＜∞且ｒ（ｔ）＞０，∫＋∞ｒ（ｓ）ｄｓ＝∞成立，则当ｔ充分大时Ｌｏｇｉｓｔｉｃ方程的任一非零解一定进入区间（ｋｔ，Ｋｔ），并且任意两个初值解将任意接近。尤其当ｒ（ｔ），Ｋ（ｔ）为Ｔ—周期函数时，Ｌｏｇｉｓｔｉｃ方程存在唯一的全局渐近稳定的Ｔ—周期解。本文还给出一般时变Ｌｏｇｉｓｔｉｃ方程和周期Ｌｏｇｉｓｔｉｃ方程解的表达式。
The paper deals with some asymptotic characteristics of the solution of nonautonomous Logistic equation d x d t = r(t)x(1-xK(t)) . We denote K =sup t∈R K(t) , k =inf t∈R k(t) , if 0<k ′<k≤K<K ′<∞ , and r(t)>0 , ∫ +∞ r(s) d s=∞ is established. When t is big enough, any of non zero solutions to Logistic equations must be in an interval (k ′,K ′) , therefrom any two initial value solutions will be freely near enough. Especially when r(t), K(t) are of T- periodic functions, Logistic equations will have unique globally and asymptotially stable T- periodic solutions. Also, the paper gives the expressions of the solutions to the nonautonomous and periodic Logistic equations.(Received on Sep.19, 1997)
出处
《辽宁工学院学报》
1998年第1期72-74,共3页
Journal of Liaoning Institute of Technology(Natural Science Edition)
基金
辽宁省教委科研基金
关键词
时变
LOGISTIC方程
渐近性态
周期解
nonautonomous Logistic equation
asymptotic characteristic
periodic solution
sustainable living
last solution
