具有白噪聲的離散FitzHugh-Nagumo方程在加權(quán)空間中的全局吸引子.pdf

1、揚(yáng)州大學(xué)碩士學(xué)位論文具有白噪聲的離散FitzHughNagumo方程在加權(quán)空間中的全局吸引子姓名：朱鑫銓申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：劉玉榮20070401揚(yáng)州大學(xué)碩士學(xué)位論文2一AbstractInthispaper，weinvestigatetheexistenceofglobalrandomattractorsoftherandom倦=‰也嗨1)地)一uq警，=占“一7葉)，(1)FirstlyWeestablishH

2、ilbertspaceC2“‘2andprovetheexistenceanduniquenessofthesolutionsoftherandomlatticeFitzHughNagumosysteminthespace譬譬Furthermore，basedonthemethodofstochasticanalysis，weshowthatthesolutionsofequationdependcontinuouslyoninitia

3、lconditionsandestimatethe“ends’’ofsolutionsofoursystemThenWeestablishtheexistenceoftheglobalrandomatWacturwiththesetoftemperedboundedsetsbyprovingtheasymptoticcompactnessoftherandomdynamicalsystemsInsection1，Westatetheba

4、ckgroundofstochasticdynamicalsystemsInSection2，wegivesomebasicconceptsrelatedtostochasticdynamicalsystemsandtheglobalrandomattractorandpresentsomenotationsandgiveasimpledescrip。tionofthesystemInSection3，Someboundedcondit

5、ionsandassumptionsofnonlineartermsaregivenandtheexistenceanduniquenessofsolutionsofsystem(1)areestablishedInSection4，weprovetheexistenceoftheabsorbingsetsInSection5，bysomeresultsof[6]，weshowthattheexistenceofglobalrandom