Mobility and equilibrium stability analysis of pin-jointed mechanisms with equilibrium matrix SVD

Under certain load pattern, the geometrically indeterminate pin-jointed mechanisms will present certain shapes to keep static equalization. This paper proposes a matrix-based method to determine the mobility and equilibrium stability of mechanisms according to the effects of the external loads. The first and second variations of the potential energy function of mechanisms under conservative force field are analyzed. Based on the singular value decomposition (SVD) method, a new crite- rion for the mobility and equilibrium stability of mechanisms can be concluded by analyzing the equilibrium matrix. The mobility and stability of mechanisms can be classified by unified matrix formulae. A number of examples are given to demonstrate the proposed criterion. In the end, criteria are summarized in a table.

Controlling chaos in power system based on finite-time stability theory

Recent investigations show that a power system is a highly nonlinear system and can exhibit chaotic behaviour leading to a voltage collapse, which severely threatens the secure and stable operation of the power system. Based on the finite-time stability theory, two control strategies are presented to achieve finite-time chaos control. In addition, the problem of how to stabilize an unstable nonzero equilibrium point in a finite time is solved by coordinate transformation for the first time. Numerical simulations are presented to demonstrate the effectiveness and the robustness of the proposed scheme. The research in this paper may help to maintain the secure operation of power systems.

Slope stability analysis of Southern slope of Chengmenshan copper mine,China

The engineering geology and hydrogeology in the southern slope of Chengmenshan copper mine are very complicated,because there is a soft-weak layer between two kinds of sandstones.Field investigations demonstrate that some instability problems might occur in the slope.In this research,the southern slope,which is divided into six sections(I-0,I-1,I-2,II-0,II-1 and II-2),is selected for slope stability analysis using limit equilibrium and numerical method.Stability results show that the values of factor of safety(FOS) of sections I-0,I-1 and I-2 are very low and slope failure is likely to happen.Therefore reinforcement subjected to seismic,water and weak layer according to sections were carried out to increase the factor of safety of the three sections,two methods were used;grouting with hydration of cement and water to increase the cohesion(c) and pre-stressed anchor.Results of reinforcement showed that factor of safety increased more than 1.15.

STABILITY OF AN SEIS EPIDEMIC MODEL WITH CONSTANT RECRUITMENT AND A VARYING TOTAL POPULATION SIZE

This paper considers an SEIS epidemic model with infectious force in the latent period and a general population-size dependent contact rate. A threshold parameter R is identified. If R≤1, the disease-free equilibrium O is globally stable. If R〉1, there is a unique endemic equilibrium and O is unstable. For two important special cases of bilinear and standard incidence ,sufficient conditions for the global stability of this endemic equilibrium are given. The same qualitative results are obtained provided the threshold is more than unity for the corresponding SEIS model with no infectious force in the latent period. Some existing results are extended and improved.

Stability Analysis of Bubonic Plague Model with the Causing Pathogen Yersinia pestis in the Environment

Bubonic plague is a serious bacterial disease, mainly transmitted to human beings and rodents through flea bite. However, the disease may also be transmitted upon the interaction with the infected materials or surfaces in the environment. In this study, a deterministic model for bubonic plague disease with Yersinia pestis in the environment is developed and analyzed. Conditions for existence and stability of the equilibrium points are established. Using Jacobian method disease free equilibrium (DFE) point, E0 was proved to be locally asymptotically stable. The Metzler matrix method was used to prove that the DFE was globally asymptotically stable when R0 < 1. By applying Lyapunov stability theory and La Salles invariant principle, we prove that the endemic equilibrium point of system is globally asymptotically stable when R0 > 1. Numerical simulations are done to verify the analytical predictions. The results show that bubonic plague can effectively be controlled or even be eradicated if efforts are made to ensure that there are effective and timely control strategies.

THE BOUNDED EXTERMINATION AND STABILITY OF MUTUAL INTERFERENCE SYSTEM OF FOUR－DIMENSIONAL SPECIES

This paper considers a typical mutual interference system of four-dimensionalspecies, its bounded, extermination stability are studied, and their necessary-sufficientcondition are given, and their ecology meaning set forth.

A Restricted SIR Model with Vaccination Effect for the Epidemic Outbreaks Concerning COVID-19

This paper presents a restricted SIRmathematicalmodel to analyze the evolution of a contagious infectious disease outbreak(COVID-19)using available data.The new model focuses on two main concepts:first,it can present multiple waves of the disease,and second,it analyzes how far an infection can be eradicated with the help of vaccination.The stability analysis of the equilibrium points for the suggested model is initially investigated by identifying the matching equilibrium points and examining their stability.The basic reproduction number is calculated,and the positivity of the solutions is established.Numerical simulations are performed to determine if it is multipeak and evaluate vaccination’s effects.In addition,the proposed model is compared to the literature already published and the effectiveness of vaccination has been recorded.

Reduced Differential Transform Method for Solving Nonlinear Biomathematics Models

In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.The reduced differential transforms method(RDTM)is one of the interesting methods for finding the approximate solutions for nonlinear problems.We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model.We discuss the numerical results at some special values of parameters in the approximate solutions.We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions.Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.

Research on viral dynamic models of hepatitis B virus infection

A mathematical model with cytotoxic cells of hepatitis B virus (HBV)infection is set up based on a basic model of virus dynamics without cytotoxic cells andexperimental observation of anti-viral drag therapy for HBV infection patients. A quantitativeanalysis of dynamic behaviors shows that the model has three kinds of equilibrium points, whichrepresent the patient's complete recovery without immune ability, complete recovery with immuneability, and HBV persistent infection at the end of the treatment with drag lamivudine,respectively. Our model may provide possible quantitative interpretations for the treatments ofchronic HBV infections with the drag lamivudine, in particularly explain why the plasma virus ofNowak et al. 's patients turnover the original level after stopping the lamivudine treatment.

OPTIMAL HARVESTING POLICY AND STABILITY FOR SINGLE-SPECIES GROWTH MODEL WITH STAGE STRUCTURE

Abstract. In this paper, we consider a stage structure population model with two lifestages, immature and mature, with harvesting mature population and stocking immaturepopulation. It is shown that under suitable hypotheses there exists a globally asymptoti-cally stable positive equilibrium. The effect of the delay on the populations at equilibriumand the optimal harvesting policy for mature population are also considered.

Aircraft nonlinear stability analysis and multidimensional stability region estimation under icing conditions

Icing is one of the crucial factors that could pose great threat to flight safety,and thus research on stability and stability region of aircraft safety under icing conditions is significant for control and flight.Nonlinear dynamical equations and models of aerodynamic coefficients of an aircraft are set up in this paper to study the stability and stability region of the aircraft under an icing condition.Firstly,the equilibrium points of the iced aircraft system are calculated and analyzed based on the theory of differential equation stability.Secondly,according to the correlation theory about equilibrium points and the stability region,this paper estimates the multidimensional stability region of the aircraft,based on which the stability regions before and after icing are compared.Finally,the results are confirmed by the time history analysis.The results can give a reference for stability analysis and envelope protection of the nonlinear system of an iced aircraft.

Stability Analysis of Two-Point Mooring Autonomous Underwater Vehicle

Static stability analysis of the two-point mooring autonomous underwater vehicle(AUV) is presented.The mathematic model is a set of equilibrium equations describing the attitude of the AUV.The mooring lines are regarded as inelastic catenaries,and five degrees of freedom of AUV are considered.The stability of the system is represented by inequality conditions between several physical quantities and the corresponding limitations.We analyze stability of the prime AUV and find that the AUV has a flow-following tendency,which makes the swing angle big.The result shows that the two-point mooring AUV can remain stable under 2.5 kn ocean current speed,and it will weigh anchor when the speed is greater than 3 kn.Subsequent parametric study reveals the influence of the designing parameters on the stability.

Dynamic model of tuberculosis considering multi-drug resistance and their applications

Infectious diseases have always been a problem that threatens people's health and tuberculosis is one of the major.With the development of medical scientific research,drug-resistant infectious diseases have become a more intractable threat because various drugs and antibiotics are widely used in the process of fighting against infectious diseases.In this paper,an improved dynamic model of infectious diseases considering population dynamics and drug resistance is established.The feasible region,equilibrium points and stability of the model are analyzed.Based on the existing data,this model can predict the development of the epidemic situation through numerical simulation,and put forward some relevant measures and suggestions.

Strategically supported cooperation in dynamic games with coalition structures

The problem of strategic stability of long-range cooperative agreements in dynamic games with coalition structures is investigated. Based on imputation distribution procedures, a general theoretical framework of the differential game with a coalition structure is proposed. A few assumptions about the deviation instant for a coalition are made concerning the behavior of a group of many individuals in certain dynamic environments.From these, the time-consistent cooperative agreement can be strategically supported by ε-Nash or strong ε-Nash equilibria. While in games in the extensive form with perfect information, it is somewhat surprising that without the assumptions of deviation instant for a coalition, Nash or strong Nash equilibria can be constructed.