Abstract
In this paper, a stochastic averaging method is derived for a class of non-linear stochastic systems under parametrical Poisson white noise excitation, which may be used to model the beam-beam interaction models in particle accelerators. The averaged Generalized Fokker-Planck equation is derived and the approximate stationary solution of the averaged Generalized Fokker-Planck equation is solved by using perturbation method. The present method applied in this paper can reduce the dimensions of stochastic ODE from 2n to n, which simplify the complex stochastic ODE, and then the analytical stationary solutions can be obtained. An example is employed to demonstrate the procedure of our proposed method. The analytical solution of approximate stationary probability density function is obtained, and the theoretical results are verified through numerical simulations. Finally, the stability of the amplitude process is investigated.
| Original language | English |
|---|---|
| Pages (from-to) | 277-291 |
| Number of pages | 15 |
| Journal | CMES - Computer Modeling in Engineering and Sciences |
| Volume | 93 |
| Issue number | 4 |
| State | Published - 2013 |
Keywords
- Generalized Fokker-Planck equation
- Poisson white noise
- Stationary probability density
- Stochastic averaging
- Stochastic stability