Asymptotic Weighted Periodic Oscillations for Dynamic Systems Caused by Impulse and Time Delay

It is known that the impulse and time delay can all bring oscillations to a system, which troubles the engineers time and time. So it is a meaningful matter to reveal the inherent mechanism of the system itself, particularly, the key point is to reveal the relationship between the required parameters and the asymptotic behavior of the system. To this end, a partial differential equation with impulse and time-delay is considered by using a new iteration scheme. The results show that the solution oscillates in a particular manner - it has some "asymptotic weighted-periodicity", provided that the impulse, the time-delay and the coefficients of the equation meet a certain condition.