The paper is concerned with stabilization of a scalar delay differention equation ẋ(t)− m ∑ k=1 Ak(t)x[hk(t)] = 0, t ≥ 0, x(ξ) = φ(ξ), ξ < 0, by introducing impulses in certain moments of time x(τj) = Bjx(τj − 0), j = 1, 2, . . . . Explicit stability results are presented both for the equation with positive coefficients and for the equation with Ak being of arbitrary sign. Supported by Israel M...

Delay discounting, which refers to the phenomenon that rewards decrease in subjective value as the delay associated with their receipt increases, is a paradigm that has been used extensively in substance abuse research to understand impulsive decision making. One common measure to assess delay discounting is the Monetary Choice Questionnaire (MCQ) developed by Kirby, Petry, and Bickel (1999). W...

It is characteristic for a linear ordinary differential equation that if any solution is bounded on the half-line for any bounded right-hand side then a solution of the corresponding homogeneous equation tends to zero exponentially [1]. The connection of boundedness with exponential behavior of solutions for impulsive differential equations is studied in [2,3] and many other papers. It turns ou...

In this paper, a class of impulsive bi-directional associative memory (BAM) neural networks with time-varying delays is investigated. By employing the delay differential inequality with impulsive initial conditions and M -matrix theory, some new sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive BAM neural networks with t...

This paper investigates the stability of stochastic delay differential systems with two kinds of impulses, that is, destabilizing impulses and stabilizing impulses. Both the pth moment and almost sure exponential stability criteria are established by using the average impulsive interval.When the impulses are regarded as disturbances, a lower bound of average impulsive interval is obtained; it m...

In this paper, we consider the controllability problems for a class of impulsive fractional partial neutral quasilinear functional differential inclusions with infinite delay and (α, x)-resolvent family. In particular, a set of sufficient conditions are derived for the approximate controllability of nonlinear impulsive fractional dynamical systems by assuming the associated linear system is app...

Abstract It has become imperative in recent times to determine the properties of the solutions of certain mathematical equations or inequalities from the knowledge of associated inequalities or equations. In this paper, a number of oscillatory properties of the solutions of impulsive differential inequalities are established using the knowledge of those of their associated equations and what is...

In this paper we give a nonoscillation criterion for half-linear equations with periodic coefficients under fixed moments of impulse actions. The method is based on existence of positive solutions of the related Riccati equation and a recently obtained comparison principle. In the special case when the equation becomes impulsive Hill equation new oscillation criteria are also obtained.

* 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...