Persistence, contractivity and global stability in logistic equations with piecewise constant delays |
| |
Authors: | Yoshiaki Muroya |
| |
Affiliation: | Department of Mathematical Sciences, Waseda University, Ohkubo 3-4-1 Shinjuku-ku, Tokyo, 169-8555, Japan |
| |
Abstract: | We establish sufficient conditions for the persistence and the contractivity of solutions and the global asymptotic stability for the positive equilibrium N*=1/(a+∑i=0mbi) of the following differential equation with piecewise constant arguments: where r(t) is a nonnegative continuous function on [0,+∞), r(t)0, ∑i=0mbi>0, bi0, i=0,1,2,…,m, and a+∑i=0mbi>0. These new conditions depend on a,b0 and ∑i=1mbi, and hence these are other type conditions than those given by So and Yu (Hokkaido Math. J. 24 (1995) 269–286) and others. In particular, in the case m=0 and r(t)≡r>0, we offer necessary and sufficient conditions for the persistence and contractivity of solutions. We also investigate the following differential equation with nonlinear delay terms: where r(t) is a nonnegative continuous function on [0,+∞), r(t)0, 1−ax−g(x,x,…,x)=0 has a unique solution x*>0 and g(x0,x1,…,xm)C1[(0,+∞)×(0,+∞)××(0,+∞)]. |
| |
Keywords: | Persistence Contractivity Global stability Logistic equation with piecewise constant delays |
本文献已被 ScienceDirect 等数据库收录! |
|