1. Approximating the Density of Random Differential Equations with Weak Nonlinearities via Perturbation Techniques.
- Author
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Cortés, Juan-Carlos, López-Navarro, Elena, Romero, José-Vicente, and Roselló, María-Dolores
- Subjects
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MAXIMUM entropy method , *PROBABILITY density function , *NONLINEAR oscillators , *DIFFERENTIAL equations , *DUFFING oscillators , *MAXIMUM principles (Mathematics) , *STOCHASTIC processes , *GAUSSIAN processes - Abstract
We combine the stochastic perturbation method with the maximum entropy principle to construct approximations of the first probability density function of the steady-state solution of a class of nonlinear oscillators subject to small perturbations in the nonlinear term and driven by a stochastic excitation. The nonlinearity depends both upon position and velocity, and the excitation is given by a stationary Gaussian stochastic process with certain additional properties. Furthermore, we approximate higher-order moments, the variance, and the correlation functions of the solution. The theoretical findings are illustrated via some numerical experiments that confirm that our approximations are reliable. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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