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Continuous Dependence for Stochastic Functional Differential Equations with state-dependent Regime-Switching on Initial Values

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Acta Mathematica Sinica,English Series 2021年第3期37卷 389-407页

作者： Jing Hai SHAO Kun ZHAO Center for Applied Mathematics Tianjin UniversityTianjin 300072P.R.China

This work is concerned with the continuous dependence on initial values of solutions of stochastic functional differential equations(SFDEs) with state-dependent regime-switching. Due to the state-dependence, this problem is very different to the corresponding problem for SFDEs without switching or SFDEs with Markovian switching. We provide a method to overcome the intensive interaction between the continuous component and the discrete component based on a subtle application of Skorokhod’s representation for jumping processes. Furthermore, we establish the strong convergence of Euler–Maruyama’s approximations, and estimate the order of error. The continuous dependence on initial values of Euler–Maruyama’s approximations is also investigated in the end.

关键词： Regime-switching state-dependent Euler–Maruyama’s approximation

Light-tailed behavior of stationary distribution for state-dependent random walks on a strip

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Frontiers of Mathematics in China 2014年第4期9卷 813-834页

作者： Wenming HONG Meijuan ZHANG Yiqiang Q. ZHAO School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems Beijing Normal University Beijing 100875 China School of Statistics and Mathematics Central University of Finance and EconomicsBeijing 100081 China School of Mathematics and Statistics Carleton University Ottawa Ont K1S 5B6 Canada

We consider the state-dependent reflecting random walk on a half- strip. We provide explicit criteria for （positive） recurrence, and an explicit expression for the stationary distribution. As a consequence, the light-tailed behavior of the stationary distribution is proved under appropriate conditions. The key idea of the method employed here is the decomposition of the trajectory of the random walk and the main tool is the intrinsic branching structure buried in the random walk on a strip, which is different from the matrix-analytic method.

关键词： Random walk on a strip stationary distribution light-tailedbehavior branching process recurrence state-dependent

Harvesting on a state-dependent Time Delay Model

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Journal of Systems Science and Information 2020年第1期11卷 82-96页

作者： Ruijun XIE Xin ZHANG Wei ZHANG School of Statistics and Applied Mathematics Anhui University of Finance and EconomicsBengbu 233030China Department of Basic Courses Beijing Union UniversityBeijing 100101China Students’affairs Division Anhui University of Finance and EconomicsBengbu 233030China

In this paper,we propose and analyze a cooperation model with harvesting and statedependent delay,which is assumed to be an increasing function of the population density with lower and upper *** main purpose of this article is to obtain the dynamics of our model analytically by controlling the *** present results on positivity and boundedness of all *** for the existence of all equilibria and uniqueness of a positive equilibrium are given by controlling the ***,the global exponentially asymptotical stability criteria of model is obtained by the improved Hanalay inequality.

关键词： state-dependent delay exponential asymptotic stability harvesting

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International Journal of Organic Chemistry 2012年第3期2卷 224-232页

作者： Karel D. Klika Department of Chemistry University of Turku Turku Finland

Deficiencies in the terminology used to describe chiral systems exist for behaviors under various processes and thus a more general, robust terminology is considered. For example, the descriptions for characterizing melting point, solubility, and recrystallization behaviors were adopted well before it was realized that perturbation of the enantiomeric com-position (ec) due to self-disproportionation could be effected by processes other than recrystallization such as sublimation, chromatography over achiral substrates, and even distillation. Thus, an endeavor has been made to address the question of universally describing behaviors under processes that effect, or are dependent on, the ec. The main terms that have been defined with respect to behavior are homomate (analogous to a conglomerate), heteromate, bimate (analogous to a racemic compound), and unimate (analogous to a solid solution) and they apply to melting point, solubility, recrystallization, sublimation, distillation, and chromatographic processes. Additionally, suggestions for improving the terminology for describing the states of chiral systems are also considered and the defined terms are: holemate (hol, ec = 100%), scalemate (scl, 50% ec eqm, ec = 50%).

关键词： Stereochemistry Terminology Chirality state-dependent Behavior Conglomerate Racemate

Quadratic Stabilization of Switched Uncertain Linear Systems: A Convex Combination Approach

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IEEE/CAA Journal of Automatica Sinica 2019年第5期6卷 1116-1126页

作者： Yufang Chang Guisheng Zhai Bo Fu Lianglin Xiong the School of Electrical and Electronic Engineering Hubei University of TechnologyWuhan 430068China the Department of Mathematical Sciences Shibaura Institute of TechnologySaitama 337-8570Japan the School of Mathematics and Computer Science Yunnan Minzu UniversityKunming 650500China

We consider quadratic stabilization for a class of switched systems which are composed of a finite set of continuoustime linear subsystems with norm bounded uncertainties. Under the assumption that there is no single quadratically stable subsystem, if a convex combination of subsystems is quadratically stable, then we propose a state-dependent switching law, based on the convex combination of subsystems, such that the entire switched linear system is quadratically stable. When the state information is not available, we extend the discussion to designing an outputdependent switching law by constructing a robust Luenberger observer for each subsystem.

关键词： Convex combination limear matrix inequalities (LMIs) norm bounded uncertainties output-dependent switching, quadratic stabilization state-dependent switching switched uncertain linear systems(SULS)

Telecloning Quantum states with Trapped Ions

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Communications in Theoretical Physics 2007年第5X期48卷 827-830页

作者： YANG Rong-Can LI Hong-Cai LIN Xiu HUANG Zhi-Ping School of Physics and OptoElectronics Technology Fujian Normal University Fuzhou 350007 China

We propose a scheme for telecloning quantum states with trapped ions. The scheme is based on a single ion interacting with a single laser pulse. In the protocol, an ion is firstly measured to determine whether the telecloning succeeds or not, and then another ion is detected to complete the whole procedure. The required experimental techniques are within the scope of what can be obtained in the ion-trap setup.

关键词： telecloning W states state-dependent trapped ions

Output tracking of delayed logical control networks with multi-constraint

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Frontiers of Information Technology & Electronic Engineering 2020年第2期21卷 316-323页

作者： Ya-ting ZHENG Jun-e FENG School of Mathematicst Shandong University Jinan 250100China

In this study,the output tracking of delayed logical control networks(DLCNs)with state and control constraints is further *** with other delays,state-dependent delay updates its value depending on the current state values and a pseudo-logical *** constraints mean that state values are constrained in a nonempty set and the design of the controller is *** the semi-tensor product of matrices,dynamical equations of DLCNs are converted into an algebraic description,and an equivalent augmented system is *** on the augmented system,the output tracking problem is transformed into a set stabilization problem.A deformation of the state transition matrix is computed,and a necessary and sufficient condition is derived for the output tracking of a DLCN with *** condition is easily verified by mathematical *** addition,the admissible state-feedback controller is designed to enable the outputs of the DLCN to track the reference ***,theoretical results are illustrated by an example.

关键词： Logical control networks Multi-constraint Output tracking Stabilization state-dependent delay Semi-tensor product