Geodesic
Qualitative Properties of a Duffing System with Polynomial Nonlinearity
Informatics and Automation, Differential equations and dynamical systems, Tome 308 (2020), pp. 197-209

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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. 
@article{TRSPY_2020_308_a13,
     author = {A. N. Kanatnikov and A. P. Krishchenko},
     title = {Qualitative {Properties} of a {Duffing} {System} with {Polynomial} {Nonlinearity}},
     journal = {Informatics and Automation},
     pages = {197--209},
     publisher = {mathdoc},
     volume = {308},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2020_308_a13/}
}
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A. N. Kanatnikov; A. P. Krishchenko. Qualitative Properties of a Duffing System with Polynomial Nonlinearity. Informatics and Automation, Differential equations and dynamical systems, Tome 308 (2020), pp. 197-209. http://geodesic.mathdoc.fr/item/TRSPY_2020_308_a13/