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2002•Unpublished venueRequires access

Extensions of classical averaging techniques to delay differential equations

Brad Lehman, V.B. Kolmanovskii

Open publisher page 8 citations

Abstract

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.>

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What this paper is about

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.>

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OpenAlex reports 8 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

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.>

Key concepts: Delay differential equation, Differential equation, Mathematics, Differential (mechanical device), Lyapunov function, Applied mathematics, Mathematical analysis, Physics

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