| 分数Brown运动时变随机种群收获系统数值解的均方散逸性 |
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| 引用本文： | 李强,张启敏,辛志贤. 分数Brown运动时变随机种群收获系统数值解的均方散逸性[J]. 数学的实践与认识, 2017, 0(2): 176-183 |
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| 作者姓名： | 李强 张启敏 辛志贤 |
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| 作者单位： | 1. 北方民族大学 数学与信息科学学院,宁夏 银川,750021;2. 北方民族大学 数学与信息科学学院,宁夏 银川 750021;宁夏大学 数学与计算机学院,宁夏 银川 750021 |
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| 基金项目： | 国家自然科学基金(11261043;11461053)，宁夏自然科学基金(NZ14048) |
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| 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.
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| 关 键 词： | 分数Brown运动 Bellman-Gronwall-Type 补偿倒向Euler方法 均方散逸 |
Mean-square Dissipativity of Numerical Methods for Time-Varying Stochastic Population Harvest System with Fractional Brown Motion |
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| LI Qiang,ZHANG Qi-min,XIN Zhi-xian. Mean-square Dissipativity of Numerical Methods for Time-Varying Stochastic Population Harvest System with Fractional Brown Motion[J]. Mathematics in Practice and Theory, 2017, 0(2): 176-183 |
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| Authors: | LI Qiang ZHANG Qi-min XIN Zhi-xian |
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| Abstract: | In this paper,a class of Time-Varying Stochastic Population Harvest System with fractional Brown motion is considered.By using It(o)'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. |
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| Keywords: | fractional Brownian motion Bellman-Gronwall-type estimates compensated backward Euler method mean-square dissipativity |
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