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Abstract
Impulsive differential equations arise naturally in the description of Physical systems that are subjected to sudden changes in their states. Most often the dynamics take place during afinite time interval.Impulsive differential equations arise naturally in the description of physical
systems that are subjected to sudden changes in their states. Most often the
dynamics take place during a finite time interval. Most scientific problems and
phenomena are modeled by impulsive differential equations: For examples, biological
systems such as heart beats, blood flows, population dynamics, theoretical
physics, radiophysics, pharmacokinetics, mathematical economy, chemical
technology, electric technology, metallurgy, ecology, industrial robotics,
biotechnology, medicine and so on. This leads to the study of impulsive differential
equations.Impulsive differential equations, that is, differential equations involving impulse
effect, appear as a natural description of observed evolution phenomena
of several real world problems. There are many good monographs on the impulsive
differential equations [1, 11-15]. Many processes studied in applied
sciences are represented by differential equations. However, the situation is
quite different in many physical phenomena that have a sudden change in
their states such as mechanical systems with impact, biological systems such
as heart beats, blood flows, population dynamics [16,39], theoretical physics,
radiophysics, pharmacokinetics, mathematical economy, chemical technology,
electric technology, metallurgy, ecology, industrial robotics, biotechnology processes,
chemistry [17], engineering [3], control theory [21,37], medicine [2,28]
and so on. Adequate mathematical models of such processes are systems of
differential equations with impulses. The theory of impulsive differential equations
is a new and important branch of differential equations.