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Existence and Uniqueness Results for Quaternion-Valued Nonlinear Impulsive Differential Systems

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Journal of Systems Science & Complexity 2018年第3期31卷 596-607页

作者： ZHU Jingwen sun jitao Department of Mathematics Tongji University Shanghai 200092 China College of Mathematics and Physics Jinggangshan University Jinggangshan 343009 China Institute for Intelligent Systems University of Johannesburg South Africa.

This paper studies the existence and uniqueness conditions for the quaternion-valued non-linear impulsive system. Firstly, a space of quaternion-valued piecewise functions is constructed and completeness of the space is also proved. Then by taking advantage of the Bielecki norm and fixed point theorem, existence and uniqueness criteria of quaternion-valued nonlinear impulsive system are obtained. At last, an example is given to illustrate our theoretical results.

关键词： Differential equations, existence and uniqueness, impulsive system quaternion-valued

Analysis of epidemic spreading with feedback mechanism in weighted networks

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International Journal of Biomathematics 2015年第1期8卷 81-91页

作者： Jiancheng Zhang jitao sun Department of Mathematics Tongji University Shanghai 200092 P. R. China

In this paper, we investigate a new model with a generalized feedback mechanism in weighted networks. Compare to previous models, we consider the initiative response of people and the important impact of nodes with different edges on transmission rate as epidemics prevail. Furthermore, by constructing Lyapunov function, we prove that the disease-free equilibrium E^0 is globally asymptotically stable as the epidemic threshold R^＊〈 1. When R^＊〉 1, we obtain the permanence of epidemic and the local stability of endemic equilibrium E＊. Finally, one can find a good agreement between numerical simulations and our analytical results.

关键词： SIS model weighted network feedback mechanism global analysis

STABILITY OF IMPULSIVE LINEAR HYBRID SYSTEMS WITH TIME DELAY

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Journal of Systems Science & Complexity 2010年第4期23卷 738-747页

作者： Yu ZHANG·jitao sun Department of Mathematics,Tongji University,Shanghai 200092,China. jitaosun Department of Mathematics Tongji University

This paper investigates the stability of impulsive linear hybrid systems with time *** a number of delay-independent/delay-dependent stability criteria are obtained by using Lyapunovfunctions or Lyapunov *** examples ... 详细信息

关键词： Impulsive linear hybrid system Lyapunov function Lyapunov functional time delay.

A delayed SEIRS epidemic model with impulsive vaccination and nonlinear incidence rate

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International Journal of Biomathematics 2014年第3期7卷 149-162页

作者： Jiancheng Zhang and jitao sun Department of Mathernatics Tongji University Shanghai 200092 P. R. China

In this paper, a delayed SEIRS epidemic model with nonlinear incidence rate and impul- sive vaccination is investigated. In vaccination strategy, we perform impulsive vaccina- tion of newborn infants. Using the discrete dynamic system determined by stroboscopic map, we obtain an infection-free periodic solution and establish conditions, on which the solution is globally attractive. We also conclude that the disease is permanent if the parameters of the model satisfy appropriate conditions. Finally, we illustrate the effec- tiveness of our theorems with numerical simulation. The results obtained in this paper are a good extension of the results obtained in [J. Hou and Z. Teng, Continuous and impulsive vaccination of SEIR epidemic models with saturation incidence rate, Math. Comput, Simulat. 79 （2009） 3038 3054] to the corresponding delayed SEIRS epidemic model with nonlinear incidence rate and impulsive vaccination.

关键词： SEIRS impulsive vaccination delay globally attractive permanence.

On the conjunction practical stability and controllability of large-scale impulsive control systems

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控制理论与应用（英文版） 2005年第2期3卷 181-185页

作者： Dilan GHEN jitao sun Division of Basic Courses Shanghai Maritime University Shanghai 200135China Department of Applied Mathematics Tongji University Shanghai 200092 China）

We studied the conjunction practical stability and controllability of large-scale impulsive control systems by using the comparison systems and vector Lyapunov fimctions. Then the less conservative sufficient conditio... 详细信息

关键词： Large-scale impulsive dynamic system Impulsive control Conjunction practical stability Controllability

p-th moment exponential stability of stochastic differential equations with impulse effect

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Science China(Information Sciences) 2011年第8期54卷 1702-1711页

作者： SHEN LiJuan 1,2 & sun jitao 11 Department of Mathematics, Tongji University,Shanghai 200092,China 2 Department of Mathematics,Luoyang Normal University, Luoyang 471022,China 1. Department of Mathematics Tongji University Shanghai 200092 China2. Department of Mathematics Luoyang Normal University Luoyang 471022 China

The p-th moment exponential stability of stochastic differential equations with impulse effect is *** employing the method of vector Lyapunov functions,some sufficient conditions for the p-th moment exponential stability are *** addition,the usual restriction of the growth rate of Lyapunov function is replaced by the condition of the drift and diffusion coefficients to study the p-th moment exponential *** examples are also discussed to illustrate the effectiremess of the results obtained.

关键词： stochastic differential equations impulse p-th moment exponential stability vector Lyapunov functions

Persistence in A Three Species Predator-Prey System

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Systems Science and Systems Engineering 1999年第2期9卷 203-208页

作者： sun jitao ZHANG Yinping(Iust. of Appl. Math., Shanghai Tiedao University, Shanghai 200331, China)

In this paper we consider the persistence of the following three species Lotka-Volterrapredator-prey modelIt’s proved that the Lotka-Volterra model is persistent under appropriate conditions.

关键词： persistence predator-prey system

Stability of Time-varying Linear Systems with Time Delays

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Systems Science and Systems Engineering 1996年第2期6卷 175-178页

作者： sun jitao ZHANG Yingping(Dapt.of Math.,East China Institute of Metallurgy,Maanshan,Anhui,243002,China)

Easy ways to test the stability of systems involving time delays have been *** this paper,some unconditional stability and asymptotically stable with decay rate α criteria for time-varying linear systems with time de... 详细信息

关键词： Stability of Time-varying Linear Systems with Time Delays

Robust Stabilization for Uncertain Control Systems Using Piecewise Quadratic Lyapunov Functions

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Journal of Systems Engineering and Electronics 2002年第4期13卷 56-60页

作者： Zhang Yinping & sun jitao Dept. of Appl. Math., Tongji University, Shanghai 200092, P. R. China Dept. of Appl. Math. Tongji University Shanghai 200092 P. R. China

The sufficient condition based on piecewise quadratic simultaneous Lyapunov functions for robust stabilization of uncertain control systems via a constant linear state feedback control law is obtained. The objective is to use a robust stability criterion that is less conservative than the usual quadratic stability criterion. Numerical example is given, showing the advanteges of the proposed method.

关键词： Robust State feedback control, Stabilizing uncertain system.