In this monograph as a mathematical
apparatus are used and investigated several classes of differential equations.
The most significant feature of these differential equations is the presence of
impulsive effects.
The main goals and the results achieved in the monograph are
related to the use of this class of equation for an adequate description of the
dynamics of several types of processes that are subject to discrete external
interventions and change the speed of development. In all proposed models the
following requirements have met:
1) Presented and studied mathematical models in the book are extensions
of existing known in the literature models of real objects and related
processes.
2)
Generalizations of the studied models are related to
the admission of external impulsive effects, which lead to “jump-like” change
the quantity characteristics of the described object as well as the rate of its
modification.
3) Sufficient conditions which guarantee certain qualities of
the dynamics of the quantities of the modeled objects are found.
4) Studies of the qualities of the modification of the modeled
objects are possible to be successful by differential equations with variable structure and impulsive effects.
5) The
considerations relating to the existence of the studied
properties of dynamic objects cannot be realized without introducing new
concepts and proving of appropriate theorems.
The main objectives
can be conditionally divided into several parts: 1) New classes of differential equations with
variable structure and impulses are introduced and studied; 2) Specific properties of the
above-mentioned class of differential equations are introduced and studied.
The present monograph consists of an introduction
and seven chapters. Each chapter contains several sections.