Open AccessPermanence for two-species Lotka-Volterra systems with delays
Author(s) -
Shang Lin,
Zhengyi Lu
Publication year - 2006
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2006.3.137
Subject(s) - intraspecific competition , volterra equations , competition (biology) , mathematics , pure mathematics , combinatorics , mathematical physics , physics , ecology , biology , quantum mechanics , nonlinear system
The permanence of the following Lotka-Volterra system with time delays x '(1) ( t ) = x(1) ( t ) [ r(1) - a(1)x(1) ( t ) + a(11)x(1) ( t - tau(11) ) + a(12)x(2) ( t - tau(12) ) ] x '(2) ( t ) = x(2) ( t ) [ r(2) - a(2)x(2) ( t ) + a(21)x(1) ( t - tau(21) ) + a(22)x(2) ( t - tau(22) ) ] is considered.With intraspecific competition, it is proved that in competitive case, the system is permanent if and only if the interaction matrix of the system satisfies condition (C1) and in cooperative case it is proved that condition (C2) is sufficient for the permanence of the system.