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DYNAMICAL BEHAVIOR OF A STOCHASTIC HBV INFECTION MODEL WITH LOGISTIC HEPATOCYTE GROWTH

Acta Mathematica Scientia 2017年第4期37卷 927-940页

作者：刘群蒋达清史宁中 Tasawar HAYAT Ahmed ALSAEDI School of Mathematics and Statistics Key Laboratory of Applied Statistics of MOENortheast Normal UniversityChangchun 130024China School of Mathematics and Statistics Guangxi Universities Key Lab of Complex System Optimization and Big Data ProcessingYulin Normal UniversityYulinGuangxi 537000China Nonlinear Analysis and Applied Mathematics(NAAM)Research Group Department of MathematicsFaculty of ScienceKing Abdulaziz UniversityJeddah 121589Saudi Arabia College of Science China University of Petroleum(East China)Qingdao 266580China Department of Mathematics Quaid-i-Azam University 45320Islamabad 44000Pakistan

This paper is concerned with a stochastic HBV infection model with logistic growth. First, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the HBV infection model. Then we obtain sufficient conditions for extinction of the disease. The stationary distribution shows that the disease can become persistent in vivo.

关键词： stochastic HBV infection model extinction stationary distribution Lyapunov function

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Geometric analysis and onset of chaos for the resonant nonlinear Schrödinger system

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The European Physical Journal Special Topics 2021年第11期231卷 2133-2142页

作者： Lai, Ting Feng, Chunsheng Liu, Yongjian Liu, Aimin School of Mathematics and Computational Science Xiangtan University Xiangtan People’s Republic of China Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal University Yulin People’s Republic of China

In this paper, Jacobi stability of a resonant nonlinear Schrödinger (RNS) system is studied by the KCC theory, which is also called differential geometric method. The RNS system is transformed into an equivalent planar differential system by traveling wave transformation, then the Lyapunov stability of equilibrium points of the planar system is analyzed. By constructing geometric invariants, we analyze and discuss the Jacobi stability of three equilibrium points. The results show that the zero point is always Jacobi stable, while the Jacobi stability of the other nonzero equilibrium points are determined by the values of the parameters. In addition, the focusing tendency towards trajectories around the equilibrium points are studied by the dynamical behavior of deviation vector. Finally, numerical results show that the system presents quasi-periodic and chaotic phenomena under periodic disturbances.

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Applications of Generalized Fractional Hemivariational Inequalities in Solid Viscoelastic Contact Mechanics

SSRN

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SSRN 2022年

作者： Han, Jiangfeng Li, Changpin Zeng, Shengda Department of Mathematics Shanghai University Shanghai200444 China Guangxi Colleges Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal University Guangxi 537000 China

This paper studies a generalized fractional hemivariational inequality in infinite-dimensional spaces. Under the suitable assumptions, the existence result is delivered by using the temporally semidiscrete scheme and the surjectivity result for multivalued pseudomonotone operator. As an illustrative application, we propose a frictionless contact model that describes the quasi-static contact between a viscoelastic body and a solid foundation. The viscoelastic constitutive equation is modeled by fractional Kelvin-Voigt law with ψ -Caputo derivative, and the contact condition is expressed as the Clarke subdifferential of a nonconvex and nonsmooth functional. Finally, the weak solvability of the mechanical system is obtained by using our abstract mathematical result. © 2022, The Authors. All rights reserved.

关键词： Viscoelasticity

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TIME PERIODIC SOLUTIONS TO THE EVOLUTIONARY OSEEN MODEL FOR A GENERALIZED NEWTONIAN INCOMPRESSIBLE FLUID

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Acta Mathematica Scientia 2023年第4期43卷 1645-1667页

作者：岑金夏 Stanislaw MIGóRSKI Emilio VILCHES 曾生达 School of Mathematical Sciences Zhejiang Normal UniversityJinhua 321004China Jagiellonian University in Krakow Chair of Optimization and Controlul.Lojasiewicza 630348 KrakowPoland Instituto de Ciencias de la Ingenier´ıa Universidad de O’HigginsAv.Libertador Bernardo OHiggins 6112841959 RancaguaChile Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal UniversityYulin 537000China Department of Mathematics Nanjing University Nanjing 210093China Jagiellonian University in Krakow Faculty of Mathematics and Computer Scienceul.Lojasiewicza 630348 KrakowPoland

In this paper we study a nonstationary Oseen model for a generalized Newtonian incompressible fluid with a time periodic condition and a multivalued,nonmonotone friction ***,a variational formulation of the model is obtained;that is a nonlinear boundary hemivariational inequality of parabolic type for the velocity ***,an abstract first-order evolutionary hemivariational inequality in the framework of an evolution triple of spaces is *** mild assumptions,the nonemptiness and weak compactness of the set of periodic solutions to the abstract inequality are ***,a uniqueness theorem for the abstract inequality is established by using a monotonicity ***,we employ the theoretical results to examine the nonstationary Oseen model.

关键词： nonstationary Oseen model Newtonian incompressible fluid hemivariational inequality periodic solution generalized subgradient

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The approximate parallelity of complex fuzzy sets

The approximate parallelity of complex fuzzy sets

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作者： Hu, Bo Bi, Lvqing Dai, Songsong Li, Sizhao School of Mechanical and Electrical Engineering Guizhou Normal University Guiyang China School of Electronics and Communication Engineering Guangxi Colleges Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal University Yulin China School of Information Science and Engineering Xiamen University Xiamen361005 China College of Computer Science and Technology Harbin Engineering University Harbin China

A complex fuzzy set is a set whose membership grades are complex values in the unit circle in the complex plane. This paper introduces the concept of approximate parallelity between complex fuzzy sets based on the phase of complex-valued membership grade. After that, the property of approximate parallelity preserving for complex fuzzy operators and complex fuzzy inference are investigated. © 2018 - IOS Press and the authors. All rights reserved.

关键词： Fuzzy inference

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Canard Phenomenon of the Snare-Sm Diffusive Model

SSRN

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SSRN 2024年

作者： Pan, Cuiyu Liu, Yongjian School of Mathematics and Statistics Guangxi Normal University Guilin541000 China Center for Applied Mathematics of Guangxi Guangxi Colleges Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal University Yulin537000 China

This paper is devoted to the periodic behaviors of the SNARE-SM model with weak diffusion. More precisely, with the help of geometric singular perturbation theory, we investigate theoretically the existence of relaxation oscillation and canard explosion phenomenon of the SNARE-SM diffusion model. Numerical simulations are also carried out to verify the theoretical results. These dynamic behaviors implies different modes of neurotransmitter release as the ratio of the clamping action of SNARE-SM proteins complexin to the dissociation of the involved proteins has changed. © 2024, The Authors. All rights reserved.

关键词： Proteins

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Effects of Adaptive Random Deceleration on Traffic Flow

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Journal of Applied Mathematics and Physics 2023年第3期11卷 618-628页

作者： Qi Wang Shu Zhu Liuhua Zhu School of computer Jiangsu University of Science and Technology Zhenjiang China School of Physics and Telecommunication Engineering Yulin Normal University Yulin China Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin China Optoelectronic Information Research Center Yulin Normal University Yulin China

Based on the Nagel-Schreckenberg model, an improved cellular automaton traffic flow model is proposed, in which the random deceleration probability of each vehicle is no longer fixed, but is adaptively adjusted according to the local traffic density in its vision and its current velocity. The numerical simulation results show that the maximum traffic capacity of the improved model under the same parameters is greater than that of the Nagel-Schreckenberg model, and is closer to the measured data. In addition, the traffic flow and vehicle velocity under different meteorological conditions are simulated by using the improved model, and the synchronized flow phenomenon consistent with the actual traffic is reproduced. Meanwhile, the results show that under the same parameters, when the traffic density is equal to 0.3, the traffic flow of the improved model increases by about 11% compared with the original model, and when the traffic density increases to 0.6, the traffic flow increases by about 27%. .

关键词： Traffic Flow Cellular Automaton Adaptive Random Deceleration Synchronized Flow

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Analysis of solution to an elliptic free boundary value problem equipped with a ‘bad’ data

arXiv

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arXiv 2024年

作者： Choudhuri, Debajyoti Zeng, Shengda School of Basic Sciences Indian Institute of Technology Bhubaneswar Khordha Odisha 752050 India Center for Applied Mathematics of Guangxi Guangxi Colleges Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal University Guangxi Yulin537000 China

关键词： Boundary value problems

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A hybrid MILP and IPM for dynamic economic dispatch with valve point effect

arXiv

引用

arXiv 2017年

作者： Pan, Shanshan Jian, Jinbao Yang, Linfeng College of Electrical Engineering Guangxi University Nanning530004 China Guangxi Colleges Universities Key Laboratory Complex System Optimization and Big Data Processing Yulin Normal University Yulin537000 China College of Computer Electronics and Information Guangxi University Nanning530004 China

Dynamic economic dispatch with valve-point effect (DED-VPE) is a non-convex and non-differentiable optimization problem which is difficult to solve efficiently. In this paper, a hybrid mixed integer linear programming (MILP) and interior point method (IPM), denoted by MILP-IPM, is proposed to solve such a DED-VPE problem, where the complicated transmission loss is also included. Due to the non-differentiable characteristic of DED-VPE, the classical derivative-based optimization methods can not be used any more. With the help of model reformulation, a differentiable non-linear programming (NLP) formulation which can be directly solved by IPM is derived. However, if the DED-VPE is solved by IPM in a single step, the optimization will easily trap in a poor local optima due to its non-convex and multiple local minima characteristics. To exploit a better solution, an MILP method is required to solve the DED-VPE without transmission loss, yielding a good initial point for IPM to improve the quality of the solution. Simulation results demonstrate the validity and effectiveness of the proposed MILP-IPM in solving DED-VPE. Copyright © 2017, The Authors. All rights reserved.

关键词： Wave transmission

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Solution to dynamic economic dispatch with prohibited operating zones via MILP

arXiv

引用

arXiv 2017年

作者： Pan, Shanshan Jian, Jinbao Yang, Linfeng College of Electrical Engineering Guangxi University Nanning530004 China Guangxi Colleges Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal University Yulin537000 China College of Computer Electronics and Information Guangxi University Nanning530004 China

Dynamic economic dispatch (DED) problem considering prohibited operating zones (POZ), ramp rate constraints, transmission losses and spinning reserve constraints is a complicated non-linear problem which is difficult to solve efficiently. In this paper, a mixed integer linear programming (MILP) method is proposed to solve such a DED problem. Firstly, a novel MILP formulation for DED problem without considering the transmission losses, denoted by MILP-1, is presented by using perspective cut reformulation technique. When the transmission losses are considered, the quadratic terms in the transmission losses are replaced by their first order Taylor expansions, and then an MILP formulation for DED considering the transmission losses, denoted by MILP-2, is obtained. Based on MILP-1 and MILP-2, an MILP-iteration algorithm (MILP-IA) is proposed to solve the complicated DED problem. The effectiveness of the MILP-1 and MILP-IA are assessed by several cases and the simulation results show that both of them can solve to competitive solutions in a short time. Copyright © 2017, The Authors. All rights reserved.

关键词： Wave transmission

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