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基于指数型广义反射矩阵的微分系统与周期解 被引量：2

The differential system and periodic solution based on the exponential generalized reflection matrix
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摘要 为了解决具有指数型广义反射矩阵的线性微分系统的周期解与稳定性问题,提出通过线性微分系统的广义反射矩阵来寻找其Poincaré映射的方法,研究了具有指数型广义反射矩阵的线性微分系统.x=P(t)x的条件,给出此类线性微分系统的广义反射矩阵的形式和广义反射函数,从而得到该类微分系统的周期解和稳定性.该结果对研究其他微分系统的周期解与稳定性具有一定的参考价值和指导意义. In order to solve the periodic solution and stability problem of linear differential system which has the exponential type generalized reflection matrix,this paper proposes a method seek for its Poincaré mapping by the generalized reflection matrix of the linear differential system.The author studies the condition of linear differential system =P（t）x that has the exponential type generalized reflection matrix,obtains the generalized reflection matrix form and the generalized reflection function of this kind of linear differential system,thus obtains their periodic solution and stability.This result has certain reference value and the guiding sense to study the periodic solution and the stability of other differential system.
作者 孙长军 周正新
机构地区 扬州大学数学科学学院 连云港职业技术学院
出处 《扬州大学学报（自然科学版）》 CAS CSCD 北大核心 2011年第2期15-18,共4页 Journal of Yangzhou University：Natural Science Edition
基金 国家自然科学基金资助项目(60774073) 江苏省高校自然科学基金资助项目(08KJB110013)
关键词 广义反射函数 广义反射矩阵 线性微分系统 周期解 稳定性 generalized reflection function reflection generalized matrix linear differential system periodic solution stability
分类号 O175.13 [理学—基础数学]
  • 相关文献

参考文献12

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二级参考文献36

  • 1Zhang Shanlin Zhou Zhengxin (Dept. of Math., Yangzhou University, Yangzhou 225002).ON THE EQUIVALENCE OF THE ABEL EQUATION[J].Annals of Differential Equations,2006,22(3):461-466. 被引量：3
  • 2Zhou Zheng xin Department of Mathematics, University of Yangzhou, Yangzhou 225002, Jiangsu, China.The Reflective Function of Differential System[J].Wuhan University Journal of Natural Sciences,2002,7(4):383-387. 被引量：4
  • 3Zhou ZhengxinDept.of Math.,College of Science,Yangzhou Univ.,Yangzhou 225002..REFLECTIVE FUNCTION AND PERIODIC SOLUTION OF DIFFERENTIAL SYSTEMS[J].Applied Mathematics(A Journal of Chinese Universities),2002,17(1):13-23. 被引量：7
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  • 10Veresovich P P. Nonautonomous second order quadratic system equivalent to linear system[J]. Differ Eq, 1998, 14(12): 2257-2259.

共引文献24

同被引文献17

  • 1孙长军.基于对角广义反射矩阵的线性微分系统及其周期解[J].湖北大学学报（自然科学版）,2012,34(2):226-230. 被引量：1
  • 2MIRONENKO V 1. Analysis of reflective function and multivariate differential system[M]. Gomel , Gomel Uni?versity Press, 2004: 59-ISO.
  • 3MIRONENKO V V. Time-symmetry-preserving perturbations of differential systems[J]. Differ Equ , 2004, 40(0): 1325-1332.
  • 4MIRONENKO V 1, MIRONENKO V V. Time symmetries and in-period transformations[J]. Appl Math Lett, 2011, 24(10): 1721-1723.
  • 5VERESOVICH P P. Nonautonomous second order quadratic system equivalent to linear system[J]. Differ Uravn , 1995, 14(2): 2257-2259.
  • 6MAIOROVSKAYA S V. Quadratic systems with a linear reflecting function[J]. Differ Equ, 2009, 45(2): 271- 273.
  • 7BEL'SKIl V A. On the construction of first-order polynomial differential equations equivalent to a given equation in the sense of having the same reflective function[J]. Differ Equ , 2012. 4S( 1): 11-lS.
  • 8ZHOU Zhengxin. On the symmetry and periodicity of solutions of differential systems[J]. Nonlinear Anal: Real World Appl , 2014. 17: 64-70.
  • 9ZHOU Zhengxin, TAl Richang, WANG Fei, et al. On the equivalence of differential equations[J].J Appl Anal Comput , 2014, 4(1): 103-114.
  • 10BELSKY V A. MIRONENKO V 1. Reflecting function preserving polynomial perturbations of Abel equation[J]. Prob Phys Math Tech. 2011. 9(4): 79-S5.

引证文献2

扬州大学学报（自然科学版）
2011年 第2期

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