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asymptotical behavior of ground state solutions for critical quasilinear Schrodinger equation

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Frontiers of Mathematics in China 2020年第1期15卷 21-46页

作者： Yongpeng CHEN Yuxia GUO Zhongwei TANG School of Mathematical Sciences Beijing Normal UniversityBeijing 100875China Department of Mathematics Tsinghua UniversityBeijing 100084China

This paper is concerned with the existence and asymptotical behavior of positive ground state solutions for a class of critical quasilinear Schrodinger equation.By using a change of variables and variational argument,... 详细信息

关键词： Quasilinear Schrodinger equation critical exponent ground state solution asymptotical behavior

Multiple Lagrange stability and Lyapunov asymptotical stability of delayed fractional-order Cohen-Grossberg neural networks

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Chinese Physics B 2020年第2期29卷 196-205页

作者：黄玉娇袁孝焰杨旭华龙海霞肖杰 Zhijiang College Zhejiang University of TechnologyHangzhou 310024China College of Computer Science and Technology Zhejiang University of TechnologyHangzhou 310023China

This paper addresses the coexistence and local stability of multiple equilibrium points for fractional-order Cohen-Grossberg neural networks(FOCGNNs)with time delays.Based on Brouwer's fixed point theorem,sufficient conditions are established to ensure the existence of Πi=1^n(2Ki+1)equilibrium points for FOCGNNs.Through the use of Hardy inequality,fractional Halanay inequality,and Lyapunov theory,some criteria are established to ensure the local Lagrange stability and the local Lyapunov asymptotical stability of Πi=1^n(Ki+1)equilibrium points for FOCGNNs.The obtained results encompass those of integer-order Hopfield neural networks with or without delay as special cases.The activation functions are nonlinear and nonmonotonic.There could be many corner points in this general class of activation functions.The structure of activation functions makes FOCGNNs could have a lot of stable equilibrium points.Coexistence of multiple stable equilibrium points is necessary when neural networks come to pattern recognition and associative memories.Finally,two numerical examples are provided to illustrate the effectiveness of the obtained results.

关键词： fractional-order Cohen-Grossberg neural networks multiple Lagrange stability multiple Lyapunov asymptotical stability time delays

New Results of Global asymptotical Stability for Impulsive Hopfield Neural Networks with Leakage Time-Varying Delay

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Journal of Applied Mathematics and Physics 2017年第11期5卷 2112-2126页

作者： Qiang Xi School of Mathematic and Quantitative Economics Shandong University of Finance and Economics Ji’nan China

In this paper, Hopfield neural networks with impulse and leakage time-varying delay are considered. New sufficient conditions for global asymptotical stability of the equilibrium point are derived by using Lyapunov-Kravsovskii functional, model transformation and some analysis techniques. The criterion of stability depends on the impulse and the bounds of the leakage time-varying delay and its derivative, and is presented in terms of a linear matrix inequality (LMI).

关键词： Global asymptotical Stability Hopfield Neural Networks Leakage Time-Varying Delay Impulse Lyapunov-Kravsovskii Functional Linear Matrix Inequality

Criteria for asymptotical stability independent of delay differential equation

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Journal of Harbin Institute of Technology(New Series) 1999年第4期6卷 13-15页

作者：邱深山刘明珠

０　ＩＮＴＲＯＤＵＣＴＩＯＮＴｈｉｓｎｏｔｅｄｅａｌｓｗｉｔｈｔｈｅｄｅｌａｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｄｕ（ｔ）ｄｔ＝ａｕ（ｔ）＋ｂｕ（ｔ－τ）＋ｃｕ（ｔ－２τ）（１）ｗｈｅｒｅτ≥０ａｎｄａ，ｂ，ｃ... 详细信息

０　ＩＮＴＲＯＤＵＣＴＩＯＮＴｈｉｓｎｏｔｅｄｅａｌｓｗｉｔｈｔｈｅｄｅｌａｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｄｕ（ｔ）ｄｔ＝ａｕ（ｔ）＋ｂｕ（ｔ－τ）＋ｃｕ（ｔ－２τ）（１）ｗｈｅｒｅτ≥０ａｎｄａ，ｂ，ｃａｒｅｒｅａｌｎｕｍｂｅｒｓ．Ｌｅ...

关键词： delay differential equation asymptotical stability

Stability of a linear oscillator with damping force of the fractional-order derivative

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Science China(Physics,Mechanics & Astronomy) 2010年第2期53卷 345-352页

作者： WANG ZaiHua1,2 & HU HaiYan1 1 Institute of Vibration Engineering Research,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China 2 Institute of Science,PLA University of Science and Technology,Nanjing 211101,China Institute of Vibration Engineering Research Nanjing University of Aeronautics and Astronautics Nanjing China Institute of Science PLA University of Science and Technology Nanjing China

It begins with the study of damping representation of a linear vibration system of single degree of freedom (SDOF),from the view point of fractional calculus. By using the idea of stability switch,it shows that the linear term involving the fractional-order derivative of an order between 0 and 2 always acts as a damping force,so that the unique equilibrium is asymp-totically stable. Further,based on the idea of stability switch again,the paper proposes a scheme for determining the stable gain region of a linear vibration system under a fractional-order control. It shows that unlike the classical velocity feedback which can adjust the damping force only,a fractional-order feedback can adjust not only the damping force,but also the elastic re-storing force,and in addition,a fractional-order PDα control can either enlarge the stable gain region or narrow the stable gain region. For the dynamic systems described by integer-order derivatives,the asymptotical stability of an equilibrium is guaranteed if all characteristic roots stay in the open left half-plane,while for the systems with fractional-order derivatives,the asymptotical stability of an equilibrium is guaranteed if all characteristic roots stay within a sector in the complex plane. Analysis shows that the proposed method,based on the idea of stability switch,works effectively in the stability analysis of dynamical systems with fractional-order derivatives.

关键词： vibration system fractional-order derivative asymptotical stability stability switch

Global and Bifurcation Analysis of an HIV Pathogenesis Model with Saturated Reverse Function

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Communications in Mathematical Research 2019年第4期35卷 301-317页

作者： Liu Yong-qi Meng Xiao-ying Shi Shao-yun College of Applied Mathematics Beijing Normal UniversityZhuhaiGuangdong519087 School of Statistics and Mathematics Zhongnan University of Economics and LawWuhan430073 不详

In this paper,an HIV dynamics model with the proliferation of CD4 T cells is proposed.The authors consider nonnegativity,boundedness,global asymptotic stability of the solutions and bifurcation properties of the steady states.It is proved that the virus is cleared from the host under some conditions if the basic reproduction number R0 is less than unity.Meanwhile,the model exhibits the phenomenon of backward bifurcation.We also obtain one equilibrium is semi-stable by using center manifold theory.It is proved that the endemic equilibrium is globally asymptotically stable under some conditions if R0 is greater than unity.It also is proved that the model undergoes Hopf bifurcation from the endemic equilibrium under some conditions.It is novelty that the model exhibits two famous bifurcations,backward bifurcation and Hopf bifurcation.The model is extended to incorporate the specific Cytotoxic T Lymphocytes(CTLs)immune response.Stabilities of equilibria and Hopf bifurcation are considered accordingly.In addition,some numerical simulations for justifying the theoretical analysis results are also given in paper.

关键词： HIV model global asymptotical stability center manifold theory Hopf bifurcation backward bifurcation

SOME PROBLEMS OF LYAPUNOV METHOD IN LINEAR CONTINUOUS-TIME SYSTEM

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Systems Science and Mathematical Sciences 1991年第3期4卷 244-253页

作者：黄琳许钟灵 Department of Mechanics Peking UniversityBeijing 100871China Department of Electrical and Computer Engineering University of MassachusettsAmherstM A.01003.U.S.A

In this paper,some problems of Lyapunov method in linear continuous-time systemare discussed.In part 1,some motivations are given.In part 2,in order to get a good estimate ofthe decaying time in the system,the concept of appropriate Lyapunov function is introduced andthe condition of the system is given to guarantee the existence of the appropriate Lyapunov functionAn application of the appropriate Lyapunov function is introduced to give the bound of time varyingperturbation for the stable system.In part 3,some extensions of the Lyapunov asymptotical stabilitytheorem are given,where the condition of the total derivative of the Lyapunov function along thetrajectory of the system can be reduced from negative definiteness to semi-negative definiteness andcommon quadratic forms with some reasonable conditions,the example shows the extensions areinteresting.

关键词： Appropriate Lyapunov function Uniformly complete observability Uniformly asymptotical stability

与经常的延期为一个神经网络推进功能的 Lyapunov 和延期依赖者稳定性标准的改进

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Chinese Physics B 2012年第4期21卷 183-188页

作者：邱芳张全信邓学辉 Department of Mathematics and Information Science Binzhou University Binzhou 256603 China Insititute of Differential Equation and Dynamical System Binzhou University Binzhou 256603 China

This paper investigates the asymptotical stability problem of a neural system with a constant delay. A new delaydependent stability condition is derived by using the novel augmented Lyapunov–Krasovskii function with triple integral terms, and the additional triple integral terms play a key role in the further reduction of conservativeness. Finally, a numerical example is given to demonstrate the effectiveness and lower conservativeness of the proposed method.

关键词： neural system globally asymptotical stability time delay

RESEARCHES ON THE STABILITIES OF ANALOG ELECTRONIC NEURAL NETWORKS

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Journal of Electronics(China) 1991年第2期8卷 175-179页

作者：曾黄麟虞厥邦 University of Electronic Science & Technology of China Chengdu

A new method for analyzing the stabilities of analog electronic neural networks ispresented.The energy functions with clear physical meaning are derived by introducing the staticequivalent circuit models,which has expanded the Tellegen Theorem for application on circuitanalysis.The method used to derive the energy functions of nets from first order differentialequations is valid for all first order continuous autonomous systems.The stability analysis ofcellular neural networks is made by the use of the stationary cocontent theorem.Some resultsare instructive for the network implementation on circuits.

关键词： Analog electronic neural networks Continuous autonomous systems Energy functions asymptotical stability