This article is cited in 2 papers

Qualitative Properties of a Duffing System with Polynomial Nonlinearity

A. N. Kanatnikov, A. P. Krishchenko

Bauman Moscow State Technical University, Vtoraya Baumanskaya ul. 5, Moscow, 105005 Russia

Abstract: The paper is devoted to the qualitative analysis of a nonautonomous Duffing equation with nonlinearity in the form of a monomial of odd degree. For all values of the parameters, compact localizing sets containing all compact invariant sets of the system are constructed. The behavior of the trajectories of the system outside the localizing set is analyzed, and it is shown that the trajectories of the system obey one of four scenarios.

UDC: 517.938

Received: February 17, 2019
Revised: July 14, 2019
Accepted: November 4, 2019

DOI: 10.4213/tm4055

 English version: Proceedings of the Steklov Institute of Mathematics, 2020, 308, 184–195

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