Relaxation cycles of differential-difference equations

Equations of this type are widely used in the mathematical modeling of many biophysical processes. An informative example from mathematical ecology is used below to expound ways for constructing the asymptotics of their relaxation cycles of finite amplitude, along with methods of asymptotic integration of variational equations. An important resume of our investigation: the further development of the theory of relaxation oscillations of differential-difference equations is connected with the study of examples from various areas of the natural sciences.