TY - JOUR
T1 - Permanence in kolmogorov-type systems of nonautonomous functional differential equations
AU - Tang, Baorong
AU - Kuang, Yang
N1 - Funding Information:
* Research partially supported by NSF Grant DMS 9141550. †Research partially supported by NSF Grant DMS 9102549.
PY - 1996/1
Y1 - 1996/1
N2 - In this paper we establish some general results on the permanence of the n-species Kolmogorov-type nonautonomous functional differential system ẋi = xi(t)fi(t, xt), i = 1,2,...,n. These results are applied to the n-species Lotka-Volterra-type systems with distributed delays, that is, when fi(t, xt) are linear functions of xt. Our method consists of constructing n Liapunov-like functions, which can be regarded as boundary functions of some compact region inside the positive cone in Rn.
AB - In this paper we establish some general results on the permanence of the n-species Kolmogorov-type nonautonomous functional differential system ẋi = xi(t)fi(t, xt), i = 1,2,...,n. These results are applied to the n-species Lotka-Volterra-type systems with distributed delays, that is, when fi(t, xt) are linear functions of xt. Our method consists of constructing n Liapunov-like functions, which can be regarded as boundary functions of some compact region inside the positive cone in Rn.
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U2 - 10.1006/jmaa.1996.0030
DO - 10.1006/jmaa.1996.0030
M3 - Article
AN - SCOPUS:0029690373
SN - 0022-247X
VL - 197
SP - 427
EP - 447
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -