具有可乘白噪声的非自治FitzHugh-Nagumo格点系统的随机指数吸引子

The random exponential attractor for non-autonomous FitzHugh-Nagumo lattice system with multiplicative white noise

为了得到具有可乘白噪声扰动的非自治FitzHugh-Nagumo格点系统随机指数吸引子的存在性,首先介绍了定义在无穷序列加权空间上连续余圈的随机指数吸引子存在性的充分条件;然后利用Ornstein-Uhlenbeck过程将具白噪声的FitzHugh-Nagumo格点系统转化成以随机变量为参数而无噪声的随机系统;接着分别估计该随机系统解各部分的模及某些随机变量的期望的有界性;最后得到该研究系统的随机指数吸引子的存在性.结果表明:在动力学的意义上,可以把原来为无限维的系统转化为有限维系统,它的解的渐近行为可由有限个参数来描述.

In order to obtain the existence of stochastic exponential attractors for non-autonomous FitzHugh-Nagumo lattice system with multiplicative white noise. Firstly, it was presented some sufficient conditions for the existence of a random exponential attractor for a continuous co-cycle defined on a weighted space of infinite sequences. Secondly, it was transferred the stochastic FitzHugh-Nagumo lattice system with multiplicative white noise into a random FitzHugh-Nagumo lattice system with random coefficients and without noise by the Ornstein-Uhlenbeck process. Thirdly, it was estimated the boundedness of the norm of each part and the expectations of some random variables of the solutions of the random system. Finally, it was obtained the existence of a random exponential attractor for the considered system. The results showed that in the sense of dynamics, the original system of infinite dimension could be transformed into a finite-dimensional system, the asymptotic behavior of its solution could be described by a finite number of parameters.