Polynomial Noises for Nonlinear Systems with Nonlinear Impulses and Time-Varying Delays

It is known that random noises have a significant impact on differential systems. Recently, the influences of for impulsive systems been started. Nevertheless, existing references this issue ignore phenomena nonlinear impulses and time-varying delays. Therefore, we see necessity to study with above two factors. Stimulated by above, polynomial noise introduced suppress potential explosive behavior system delay. Fortunately, stochastically controlled delay admits unique global solution, bounded, grows at most in form.