Geodesic
Qualitative Properties of a Duffing System with Polynomial Nonlinearity
Trudy Matematicheskogo Instituta imeni V.A. Steklova, 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{TM_2020_308_a13,
     author = {A. N. Kanatnikov and A. P. Krishchenko},
     title = {Qualitative {Properties} of a {Duffing} {System} with {Polynomial} {Nonlinearity}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {197--209},
     publisher = {mathdoc},
     volume = {308},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2020_308_a13/}
}
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A. N. Kanatnikov; A. P. Krishchenko. Qualitative Properties of a Duffing System with Polynomial Nonlinearity. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 308 (2020), pp. 197-209. http://geodesic.mathdoc.fr/item/TM_2020_308_a13/