Analytical and Numerical Results on Global Dynamics of the Generalized Boussinesq Equation with Cubic Nonlinearity and External Excitation

Li Mingyuan; Zhang Wei; Wu Qiliang

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Analytical and Numerical Results on Global Dynamics of the Generalized Boussinesq Equation with Cubic Nonlinearity and External Excitation

机译：Analytical and Numerical Results on Global Dynamics of the Generalized Boussinesq Equation with Cubic Nonlinearity and External Excitation

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This paper analytically and numerically presents global dynamics of the generalized Boussinesq equation (GBE) with cubic nonlinearity and harmonic excitation. The effect of the damping coefficient on the dynamical responses of the generalized Boussinesq equation is clearly revealed. Using the reductive perturbation method, an equivalent wave equation is then derived from the complex nonlinear equation of the GBE. The persistent homoclinic orbit for the perturbed equation is located through the first and second measurements, and the breaking of the homoclinic structure will generate chaos in a Smale horseshoe sense for the GBE. Numerical examples are used to test the validity of the theoretical prediction. Both theoretical prediction and numerical simulations demonstrate the homoclinic chaos for the GBE.

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《Mathematical Problems in Engineering: Theory, Methods and Applications》 |2021年第25期|6629095.1-6629095.11|共11页
作者
Li Mingyuan; Zhang Wei; Wu Qiliang;
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作者单位

Beijing Univ Technol, Beijing Key Lab Nonlinear Vibrat & Strength Mech, Beijing 100124, Peoples R China|Beijing Univ Technol, Coll Mech Engn, Beijing 100124, Peoples R China|Inner Mongolia Univ Finance & Econ, Big Data Appl Res & Collaborat Innovat Ctr, H;

Beijing Univ Technol, Beijing Key Lab Nonlinear Vibrat & Strength Mech, Beijing 100124, Peoples R China|Beijing Univ Technol, Coll Mech Engn, Beijing 100124, Peoples R China;

Tiangong Univ, Sch Artificial Intelligence, Tianjin 300387, Peoples R China|Tiangong Univ, Tianjin Key Lab Adv Technol Elect Engn & Energy, Tianjin 300387, Peoples R China;

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Analytical and Numerical Results on Global Dynamics of the Generalized Boussinesq Equation with Cubic Nonlinearity and External Excitation

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