Extensions of classical averaging techniques to delay differential equations

摘要

This paper extends the method of averaging due to Krylov and Bogoliubov (1947) and Bogoliubov and Mitropolskii (1961) to delay differential equations. Near identity change of variables are used to transform time varying delay differential equations into autonomous delay differential equations plus small perturbations. Then Lyapunov functionals are used to relate the autonomous averaged delay differential equation to the original time varying delay differential equation.