Ergodicity of stochastic Rabinovich systems driven by fractional Brownian motion

作者: Pengfei Xu , Jianhua Huang , Caibin Zeng

DOI: 10.1016/J.PHYSA.2019.122955

关键词:

摘要: Abstract The current paper is devoted to dynamics of stochastic Rabinovich systems driven by fractional Brownian motion. By using Krylov–Bogoliubov criterion and constructing Lyapunov function, the existence invariant measure system established. uniqueness also obtained strong Feller property topological irreducibility. Therefore considered possess exactly one measure, which an unique adapted stationary solution.

参考文章(16)
Aimin Liu, Lijie Li, Global dynamics of the stochastic Rabinovich system Nonlinear Dynamics. ,vol. 81, pp. 2141- 2153 ,(2015) , 10.1007/S11071-015-2131-0
Aurel Rascanu, David Nualart, Differential equations driven by fractional Brownian motion Collectanea Mathematica. ,vol. 53, pp. 55- 81 ,(2002)
V.Y. Trakhtengerts, A.S. Pikovskii, M.I. Rabinovich, Onset of stochasticity in decay confinement of parametric instability Journal of Experimental and Theoretical Physics. ,vol. 47, pp. 715- ,(1978)
Jaume Llibre, Marcelo Messias, Paulo R da Silva, On the global dynamics of the Rabinovich system Journal of Physics A. ,vol. 41, pp. 275210- ,(2008) , 10.1088/1751-8113/41/27/275210
Martin Hairer, A. Ohashi, Ergodic theory for SDEs with extrinsic memory Annals of Probability. ,vol. 35, pp. 1950- 1977 ,(2007) , 10.1214/009117906000001141
Yongjian Liu, Lijie Li, Xiong Wang, Bifurcation and attractor of the stochastic Rabinovich system with jump International Journal of Geometric Methods in Modern Physics. ,vol. 12, pp. 1550092- ,(2015) , 10.1142/S0219887815500929
Bernt Karsten Øksendal, Yaozhong Hu, Francesca Biagini, Tusheng Zhang, Stochastic Calculus for Fractional Brownian Motion and Applications ,(2010)