分数Brown运动时变随机种群收获系统数值解的均方散逸性  

Mean-square Dissipativity of Numerical Methods for Time-Varying Stochastic Population Harvest System with Fractional Brown Motion

作　　者：李强[1] 张启敏[1,2] 辛志贤[1] LI Qiang ZHANG Qi-min XIN Zhi-xian(School of Mathematics and Computer Science, Beifang University for Nationalities, Yinchuan 750021, China School Mathematics and Computer, NingXia University, Yinchuan 750021, China)

机构地区：[1]北方民族大学数学与信息科学学院,宁夏银川750021 [2]宁夏大学数学与计算机学院,宁夏银川750021

出　　处：《数学的实践与认识》2017年第2期176-183,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11261043;11461053);宁夏自然科学基金(NZ14048)

摘　　要：讨论了一类带分数Brown运动时变随机种群收获系统数值解的均方散逸性.在一定条件下,利用It公式和Bellman-Gronwall-Type引理,研究了方程(1)具有均方散逸性.分别利用带补偿的倒向Euler方法和分步倒向Euler方法讨论数值解的均方散逸性存在的充分条件,并通过数值算例对所给出的结论进行了验证.In this paper,a class of Time-Varying Stochastic Population Harvest System with fractional Brown motion is considered.By using It＇s formula and Bellman-Gronwall-type estimates,a sufficient condition is established to guarantee the mean-square dissipativity of system（1）.Then,it is shown that the mean-square dissipativity is preserved by the splitstep backward Euler method and compensated backward Euler method under a step-size constraint.Finally,the theoretical result is confirmed by a numerical experiment.

关 键 词：分数Brown运动 Bellman-Gronwall-Type 补偿倒向Euler方法 均方散逸 

分 类 号：O241.8[理学—计算数学]