Article ID Journal Published Year Pages File Type
4620711 Journal of Mathematical Analysis and Applications 2008 17 Pages PDF
Abstract

In this paper, we improve contractivity conditions of solutions for the positive equilibrium N∗=1a+∑i=0mbi of the following differential equation with piecewise constant arguments:{dN(t)dt=N(t)r(t){1−aN(t)−∑i=0mbiN(n−i)},n⩽t0andN(−j)=N−j⩾0,j=1,2,…,m, where r(t)r(t) is a nonnegative continuous function on [0,+∞)[0,+∞), r(t)≢0r(t)≢0, ∑i=0mbi>0, bi⩾0bi⩾0, i=0,1,2,…,mi=0,1,2,…,m, and a+b0>∑i=1mbi. In particular, for the case a=0a=0 and m⩾1m⩾1, we really improve the known three type conditions of the contractivity for solutions of this model (see for example, [Y. Muroya, A sufficient condition on global stability in a logistic equation with piecewise constant arguments, Hokkaido Math. J. 32 (2003) 75–83]). For the other case a≠0a≠0 and m⩾1m⩾1, under the condition ∑j=1mbj−2b0

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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