X_ρ空间上随机时滞格系统的随机动力学
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摘要
本文研究一类加性白噪声驱动的具有时滞的随机格动力系统的动力学。引入X_ρ空间,运用Hilbert空间中的基本等式和Young、Gronwall、Schwarz不等式,证明了随机时滞格点方程解的存在性、唯一性和对初值的连续依赖性,从而得到其解生成连续的无穷维随机动力系统。
The dynamics of a class of stochastic lattice dynamical systems with time delay driven by additive white noise is studied. X_ρ space is introduced, basic equalities, Young inequality, Gronwall inequality and Schwarz inequality are applied. The existence, uniqueness and continuous dependence on the initial data of solutions to the stochastic delay lattice equations with additive noise are presented. Then a continuous infinite dimensional random dynamical system generated by the solutions is obtained.
The dynamics of a class of stochastic lattice dynamical systems with time delay driven by additive white noise is studied. X_ρ space is introduced, basic equalities, Young inequality, Gronwall inequality and Schwarz inequality are applied. The existence, uniqueness and continuous dependence on the initial data of solutions to the stochastic delay lattice equations with additive noise are presented. Then a continuous infinite dimensional random dynamical system generated by the solutions is obtained.
引文
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[2] CHUA L O,ROSKA T.The CNN paradigm [J].IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applications,1993,40:147-156.
[3] KEENER J P.The effects of discrete gap junction coupling on propagation in myocardium [J].Journal of Theoretical Biology,1991,148:49-82.
[4] ERNEUX T,NICOLIS G.Propagating waves in discrete bistable reaction diffusion systems[J].Physica D,1993,67:237-244.
[5] BATES P W,LISEI H,LU K N.Attractors for stochastic lattice dynamical systems[J].Stochastics and Dynamics,2006,6:1-21.
[6] HALE J K,VERDUYN LUNEL S M.Introduction to functional differential equations[M].New York:Springer-Verlag,1993.
[7] MOHAMMED S E A.Stochastic functional differential equations[M].Boston:Pitman Advanced Publishing Program,1984.
[8] WU J.Theory and applications of partial functional differential equations[M].New York:Springer-Verlag,1996.
[9] ARNOLD L.Random dynamical systems[M].Berlin:Springer-Verlag,1998.
[10] ZHAO W,ZHANG Y.Compactness and attracting of random attractors for non-autonomous stochastic lattice dynamical systems in weighted space,?■ [J].Applied Mathematics & Computation,2016,291:226-243.