ASYMPTOTIC WEIGHTED PERIODICITY FOR DELAY DIFFERENTIAL EQUATIONS

Dieren t from studying the normal asymptotic periodicity of the solution, a new kind of asymptotic periodicity|\asymptotic weighted periodicity" of the solution is established in this paper. Accordingly, a type of dierence dieren tial equation and dierence dieren tial sys- tem with time delay are discussed. Just as shown in this paper the asymptotic weighted periodic oscillations are mainly caused by the delay. Besides of the delay eect, if the impulses are taken into consideration, then the oscillations of the solution may have some kind of asymptotic weighted periodicity, and the weight is associated with the impulse.