Rigorous continuation of periodic solutions for impulsive delay differential equations

Numerical Stability of Runge-Kutta Methods for Differential Equations with Piecewise Constant Arguments with Matrix Coefficients

“…With more and more research on delay differential equations [1][2][3][4][5], it has been widely used in various fields, such as population research [6,7], epidemiology [8,9], electrodynamics [10,11], neural network system [12,13] and so on. As a special class of delay differential equations, differential equations with piecewise constant arguments (EPCA) are difficult to solve accurately because of their complex structure.…”

Optimality and sustainability of delayed impulsive harvesting

“…In an impulsive system, whenever control is involved, it is natural to assume that the information available at the control implementation point is not up-to-date, leading to delayed impulsive conditions. The incorporation of delays in impulses goes back to the 1990s [11] with the further development of non-instantaneous impulse theory, some of which is summarized in the monographs [12,13], and with recent progress reported in [14,15,16]. Delayed impulses in the context of harvesting were explored in [17].…”

“…Thus, delayed impulsive models are of theoretical interest. While the consideration of delayed impulsive systems is not new [11], recent developments in the theory of such dynamical systems [14,15,16] have made its practical study feasible, as there are theoretical tools to investigate it. 2.…”

“…Proof. Linearizing the difference equation x n+1 = max{f (x n , x n−k ), 0} around the positive equilibrium x * given in (14) with…”