一类非线性延迟微分方程数值解的振动性分析

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一类非线性延迟微分方程数值解的振动性分析宋福义^1,2, 高建芳^1,21. 哈尔滨师范大学数学科学学院, 哈尔滨 150025;
2. 红兴隆局直中学, 双鸭山 155811 Oscillation Analysis of Numerical Solutions for a Kind of Nonlinear Delay Differential Equation SONG Fuyi^1,2, GAO Jianfang^1,21. School of Mathematical Sciences, Harbin Normal University, Harbin 150025, China;
2. Hongxinglong Juzhi Middle School, Shuangyashan 155811, China

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摘要本文考虑一类非线性延迟微分方程-带有单峰造血率的造血模型数值解的振动性及非振动性。运用线性化理论，把非线性差分方程的振动性转化为其对应的线性差分方程的振动性，通过判断线性方程的特征方程根的情况，得到了非线性差分方程振动和存在非振动解的充分条件。对于非振动的数值解，证明了非振动的数值解最终都趋于方程的平衡解。为了更有力的说明我们的结果给出了相应的算例.

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收稿日期: 2015-04-13

PACS:

O241

基金资助:黑龙江省教育厅科学技术研究（12541244）资助项目.

引用本文:

宋福义, 高建芳. 一类非线性延迟微分方程数值解的振动性分析[J]. 应用数学学报, 2016, 39(5): 762-764. SONG Fuyi, GAO Jianfang. Oscillation Analysis of Numerical Solutions for a Kind of Nonlinear Delay Differential Equation. Acta Mathematicae Applicatae Sinica, 2016, 39(5): 762-764.

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