SYSTEMS WITH AFTER-EFFECT AND RELAXATION

A system whose state is described by a scalar parameter is considered. The parameter undergoes relaxation from the initial to a critical val ue. As soon as the latter is attained, the system is instantaneously b rought back into the standard state an the relaxation process begins a gain. Because relaxation can be described by an equation with delay, e ach relaxation cycle that follows is different from the previous ones, in general. Some properties of the mathematical model under considera tion are established. In particular, conditions are given, under which the long-term behaviour of the system becomes asymptotically periodic .