In this paper, we consider the following logistic equation with piecewise constant arguments:where r > 0, a 0 , a 1 , . . . , a m 0, m j =0 a j > 0, and [x] means the maximal integer not greater than x. The sequence {N n } ∞ n=0 , where N n = N(n), n = 0, 1, 2, . . . , satisfies the difference equationUnder the condition that the first term a 0 dominates the other m coefficients a i , 1 i m, we establish new sufficient conditions of the global asymptotic stability for the positive equilibrium N * = 1/( m j =0 a j ).
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