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ON THE EXISTENCE OF SOLUTIONS TO A TYPE OF NONLINEAR DIFFERENTIAL-ITERATIVE EQUATIONS

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Chinese Annals of mathematics,Series B 2000年第2期21卷 217-224页

作者： ge WEIGAO(Department of applied mathematics, beijing institute of technology, beijing 100081, china.) LI CUIZHE(Department of applied mathematics, beijing institute of technology, beijing 100081, china.) YU YUANHONG(Inditute of applied mathematics, Acad Department of applied mathematics Beijing Institute of Technology Beijing 100081 China institute of applied mathematics Academia Sinica Beijing 100080 China

Under the assumption that h(z) is strictly monotone the existence of solutions to a type of nonlinear differential-iterative equations in the form of x’(t) = g(x(t)) -h(x(x(t))) is discussed according to the behavior... 详细信息

关键词： Differential-iterative equation Quasi-isoclinic curve Fixed point

Existence of Exactly n+1 Simple 4-Periodic Solutions of the Differential Delay Equation x(t)=-f(x(t-1))

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Acta Mathematica Sinica,English Series 1994年第1期10卷 80-87页

作者： ge Weigao Department of applied mathematics beijing institute of technology beijing,100081 china Department of applied mathematics Beijing Institute of Technology Beijing China

By discussing the zeros of *** we give in this paper a criterion for the existence of exactly n+1 simple 4-periodic solutions of the differential delay equation x(T)= -f(x(t-1)).

关键词： Existence of Exactly n+1 Simple 4-Periodic Solutions of the Differential Delay Equation x t-1

Periodic Solutions of the Differential Delay Equation (?)(t)=-f(x(t-1))

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Acta Mathematica Sinica,English Series 1996年第2期12卷 113-121页

作者： ge Weigao ge Weigao Department of applied mathematics beijing institute of technology beijing,100081 china

For an odd function f(x)defined only on a finite interval,this paper deals with the existence of periodic solutions and the number of simple periodic solutions of the differential delay equation(DDE)(?)(t)=-f(x(t-1)).By use of the method of qualitative analysis combined with the constructing of special solutions a series of interesting results are obtained on these problems.

关键词： Odd function Periodic solution Differential delay equation

On the periodic solutions of a type of differential-iterative equations

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Chinese Science Bulletin 1998年第3期43卷 204-206页

作者： ge Weigao 1, LIU Zhengrong 2 and YU Yuanhong 3 1. Department of applied mathematics, beijing institute of technology, beijing 100081, china 2. Department of mathematics, Yunnan University, Kunming 650091, china 3. institute of applied mathematics, C Department of applied mathematics Beijing Institute of Technology Beijing China Department of mathematics Yunnan University Kunming China institute of applied mathematics Chinese Academy of Sciences Beijing China

Sufficient conditions for the existence of periodic solutions to a type of nonautonomous differential_iterative equations are given.

关键词： differential_iterative equation periodic solution fixed point.

ON THE EQUATION(t) =-ax(t) + bx(x(t))(b > a > 0)

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Systems Science and Mathematical Sciences 2000年第2期13卷 195-200页

作者： SUN Weiping ge Weigao (Department of applied mathematics, beijing institute of technology, beijing 100081, china)

The existence and behavior of the solution of the differential-iterative equation x(t) =-ax(t)+bx(x(t))(b > a > 0) are studied. Some errors in [1] are corrected.

关键词： Differential-iterative equation fixed point monotone solution.

Absolute Stability of general Lurie Control Systems with Multi-Nonlinear Feedback Terms

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Acta Mathematica Sinica,English Series 2001年第4期17卷 649-656页

作者： Zuo Xin GAN Wei Gao ge institute of Systems Science, Chinese Academy of Sciences, beijing 100080, P. R. china Department of applied mathematics, beijing institute of technology, beijing 100081, P. R. china institute of Systems Science Chinese Academy of Sciences Beijing 100080 P. R. China Department of applied mathematics Beijing Institute of Technology Beijing 100081 P. R. China

In this paper, the problenl of absohlte stability for general Lurie control systems with multi- nonlinear feedback terms is investigated. From the Lyapunov function approach. new necessary and sufficient conditious and some practical sufficient conditions of absolute stability are derived. which improve the absolute stability for the set. A numerical examplc illustrates the effectiveness of the proposed results.

关键词： general Lurie system Multi-nonlinear feedback Absolute stability

一类滞后型非自治的捕食者-食饵系统的周期解

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系统科学与数学 2003年第4期23卷 461-466页

作者：董士杰葛渭高北京理工大学应用数学系

本文研究了一类滞后型三种群捕食者-食饵Lotka-Volterra系统.利用重合度理论建立了这类系统正周期解的存在性判据.

关键词：捕食者-食饵系统周期解重合度理论存在性数学生态学

STABLE RECOVERY OF SPARSELY CORRUPTED SIGNALS THROUGH JUSTICE PURSUIT DE-NOISING

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Journal of Computational mathematics 2024年第1期42卷 271-288页

作者： Ningning Li Wengu Chen Huanmin ge institute of applied Physics and Computational mathematics Beijing 100088China beijing Sport University Beijing 100084China

This paper considers a corrupted compressed sensing problem and is devoted to recover signals that are approximately sparse in some general dictionary but corrupted by a combination of interference having a sparse representation in a second general dictionary and measurement *** provide new restricted isometry property(RIP)analysis to achieve stable recovery of sparsely corrupted signals through Justice Pursuit De-Noising(JPDN)with an additional *** main tool is to adapt a crucial sparse decomposition technique to the analysis of the Justice Pursuit *** proposed RIP condition improves the existing representative *** simulations are provided to verify the reliability of the JPDN model.

关键词： Justice Pursuit De-Noising Restricted isometry property Corrupted compressed sensing Signal recovery

HOPF BIFURCATION AND CHAOS OF FINANCIAL SYSTEM ON CONDITION OF SPECIFIC COMBINATION OF PARAMETERS

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Journal of Systems Science & Complexity 2008年第2期21卷 250-259页

作者： Junhai MA Yaqiang CUI Lixia LIU Management School of Tianjin University Tianjin 300072 China Tianjin University of Finance and Economics Tianjin 300222 China

This paper studies the global bifurcation and Hopf bifurcation of one kind of complicated financial system with different parameter combinations. Conditions on which bifurcation happens, and the critical system structure when the system transforms from one kind of topological structure to another are studied as well. The criterion for identifying Hopf bifurcation under different parameter combinations is also given. The chaotic character of this system under quasi-periodic force is finally studied. The bifurcation structure graphs are given when two parameters of the combination are fixed while the other parameter varies. The presence and stability of 2 and 3 dimensional torus bifurcation are studied. All of the Lyapunov exponents of the system with different bifurcation parameters and routes leading the system to chaos with different parameter combinations are studied. It is of important theoretical and practical meaning to probe the intrinsic mechanism of such continuous complicated financial system and to find the macro control policies for such kind of system.

关键词： Chaos complicated financial system equilibrium "drift" Hopf bifurcation strange non- chaotic attractor.