Abstract :
In this paper, we consider the following logistic equation with piecewise constant arguments:
dN(t)
dt = rN(t){1− m
j=0 ajN([t − j])}, t 0, m 1,
N(0) = N0 > 0, N(−j) = N−j 0, j= 1, 2, . . .,m,
where r > 0, a0,a1, . . . , am 0, m
j=0 aj > 0, and [x] means the maximal integer not greater
than x. The sequence {Nn}∞n=0, where Nn = N(n), n = 0, 1, 2, . . . , satisfies the difference equation
Nn+1 = Nn exp r 1 −
m
j=0
ajNn−j , n= 0, 1, 2, . . . .
Under the condition that the first term a0 dominates the other m coefficients ai, 1 i m, we
establish new sufficient conditions of the global asymptotic stability for the positive equilibrium
N∗ = 1/( m
j=0 aj ).
2004 Elsevier Inc. All rights reserved
