Impulsive Differential Equations with a Small Parameter

Anti-periodic Boundary Value Problems of <i>φ</i>-Laplacian Impulsive Differential Equations

“…Impulsive differential equations have become an important aspect in some mathematical models of real processes and phenomena in science. There has a significant development in impulse theory and impulsive differential equations (see [1,2,3]). Moreover, p-Laplacian operator arises in non-Newtonian fluid flows, turbulent filtration in porous media and in many other application areas (see [5,7] and references therein).…”

On Spiking Models for Synaptic Activity and Impulsive Differential Equations

“…Note that this model includes two impulsive forcings: the increment in u and the shift of vesicles from state x to state y. Thus, in order to interpret these impulses via δ-sequences, we must include two smoothing parameters representing the fast timescales of each of these effects, 1 differential equations: Figure 6.2 shows a typical solution to (6.2) using the assumption that 2 1 . Allowing for multiple spiking events results in solutions y(t) such as those in Figure 6.3.…”

“…A separate body of mathematical literature exists where problems with abrupt forcing are represented as impulsive differential equations [2,1]. These problems have two parts: (a) a differential equation describing the smooth evolution, valid for all times apart from the isolated times t * when the impulses occur,…”

Almost Periodic Solutions of Impulsive Integro‐differential Neural Networks

“…Thus, the choice of system of neural networks accompanied with impulsive conditions would be more appropriate. For more details on impulsive differential equations and their applications, we refer the readers to [4,5,6,9,10,21,26,27].…”