The theory of impulsive differential equations is emerging as an important area of investigation, since it is a lot richer than the corresponding theory of differential equations without impulse effects. Moreover, such equations may exhibit several real world phenomena in physics, biology, engineering, etc. (see [3, 4, 20]). At the same time, the boundary value problems for impulsive differenti...

* Correspondence: [email protected]. zj.cn School of Mathematical Sciences, Xiamen University, Xiamen, 361005, PR China Abstract In this article, a new nonlinear impulsive delay differential inequality is established, which can be applied in the dynamical analysis of nonlinear systems to improve many extant results. Using the inequality, we obtain some sufficient conditions to guarantee the exponen...

For a class of impulsive predator-prey systems with Monod-Haldane functional response and seasonal effects, we investigate conditions for the local and global stabilities of prey-free solutions and for the permanence of the system by using the Flquet theory of impulsive differential equations and comparison techniques. In addition, we numerically analyze the phenomena caused by seasonal effects...