TY  - EJOU
AU  - Yue, Xiaokui  
AU  - Xu, Yong  
AU  - Yuan, Jianping  

TI  - Approximate Stationary Solution for Beam-Beam Interaction Models with Parametric Poisson White Noise
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2013
VL  - 93
IS  - 4
SN  - 1526-1506

AB  - 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.
KW  - Poisson white noise
KW  -  Stochastic averaging
KW  -  Generalized Fokker-Planck equation
KW  -  Stationary probability density
KW  -  Stochastic stability

DO  - 10.3970/cmes.2013.093.277