Global Attractor, To The Discrete Fitzhugh-nagumo Equation With White Noise In The Weighted Space

In this paper, we investigate the existence of global random attractors of the random lattice FitzHugh-Nagumo equation:Firstly, we establish Hilbert space lu 2×lu2 and prove the existence and uniqueness of the solutions of the random lattice FitzHugh-Nagumo system in the space lu 2×lu2. Furthermore, based on the method of stochastic analysis, we show that the solutions of equation depend continuously on initial conditions and estimate the"ends"of solutions of our system .Then, we establish the existence of the global random attractor with the set of tempe- red bounded sets by proving the asymptotic compactness of the random dynamical systems.In section 1, we state the background of stochastic dynamical systems .In Section 2, we give some basic concepts related to stochastic dynamical systems and the global random attractor, and present some notations and give a simple descrip- tion of the system.In Section 3, Some bounded conditions and assumptions of nonlinear terms are given, and the existence and uniqueness of solutions of system (1) are established.In Section 4, we prove the existence of the absorbing sets.In Section 5, by some results of [6], we show that the existence of global random attractor of system (1), and in this dissertation conclude with some remarks.