二次非线性项复差分方程正解的存在性分析  

Existence Analysis of Positive Solution for Second Nonlinear Term Differential Equation

作　　者：李瑞斋[1] 耿范[1] 

机构地区：[1]郑州大学西亚斯国际学院文理学院,河南新郑451150

出　　处：《科技通报》2015年第12期4-6,共3页Bulletin of Science and Technology

基　　金：VxWorks操作系统下的视频解码播放系统设计(项目编号:142102210499)

摘　　要：在动力系统理论中,二次非线性项复差分方程的正解存在性问题,在解决动力系统的稳定性控制方面具有重要意义。在相空间的一个子集上构建二次非线性项复差分方程,采用Lyapunov-Kraso-vskii泛函进行交叉项干扰的临界阈值确定,对方程正解的收敛性问题看作是时频对偶问题,通过多迹B?cklund变换,分析接收数据矩阵与阵列流型张成的空间之间的时频耦合性,得到方程的所有正解向量的递归计算式,构建差分方程的正解约束模型,进行二次非线性项复差分方程正解的稳定性证明,保证了非线性动力系统的稳定性和有界性,推导结论真实有效。In the theory of dynamical systems, quadratic nonlinear term complex difference equations for the existence of positive solution of problems and solve the stability of the power system control plays an important role in. In a subset of the phase space construction of quadratic nonlinear complex differential equations, of cross term interference in the determina-tion of threshold value by using Lyapunov Krasovskii functional, convergence problem of positive solutions of the equation as the time-frequency duality problems, through the multi track from B cklund transformation, analyzes the received data matrix and array manifold piece into the space between the time-frequency coupling, equations are obtained for all positive solutions vectors of a recursive formula, constructs difference constraint model of positive solutions of differential equations, proof of quadratic nonlinear term complex differential equation positive solution stability, to ensure the stability and bound-edness of nonlinear dynamic system, conclusion derived from the real and effective.

关 键 词：差分方程 非线性动力系统 正解 存在性 

分 类 号：O231[理学—运筹学与控制论]