A numerical study of the destabilizing effects of localized impulsive perturbations in pressuredriven Hagen-Poiseuille or pipe flow is presented. The numerics intend to ellucidate the intrinsic mechanisms of subcritical transition to turbulence in pipe flow by reproducing very recent experimental explorations carried out by Hof, Juel and Mullin [1], concluding that the minimum amplitude of a pe...

In real world, the ecological systems are usually perturbed by human exploitation activities such as planting and harvesting and so on. In order to obtain a more accurate description for such phenomenon, the impulsive differential equations play an important role. This paper is concerned with a kind of almost periodic Schoener's competition model with pure-delays and impulsive effects. By using...

where p(t) and q(t) are real-valued functions and p(t) 6= 0 for any t ∈ R. In what follows we assume that a(t), b(t), and c(t) satisfy the periodicity conditions a(t+ T ) = a(t), b(t+ T ) = b(t), c(t+ T ) = c(t), t ∈ R. The system (2) (or (3)) is said to be stable if all solutions are bounded on R, unstable if all nontrivial solutions are unbounded on R, and conditionally stable if there exits ...

This paper is mainly concerned with the dynamics of the stochastic Gilpin-Ayala model under regime switching with impulsive perturbations. The goal is to analyze the effects of Markov chain and impulse on the dynamics. Some asymptotic properties are considered and sufficient criteria for stochastic permanence, extinction, non-persistence in the mean and weak persistence are obtained. The critic...