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.

中文翻译：

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具有多项式非线性的Duffing系统的定性性质。

本文致力于对奇异单项式形式的具有非线性的非自治Duffing方程的定性分析。对于所有参数值，将构建包含系统的所有紧凑不变集的紧凑定位集。分析了系统在定位集之外的轨迹的行为，并表明系统的轨迹服从四种情况之一。