Based on Chua’s chaotic oscillation circuit, a fifth-order chaotic circuit with two memristors is designed and its corresponding dimensionless mathematic model is established. By using conventional dynamical analysis...Based on Chua’s chaotic oscillation circuit, a fifth-order chaotic circuit with two memristors is designed and its corresponding dimensionless mathematic model is established. By using conventional dynamical analysis methods, stability analysis of the equilibrium set of the circuit is performed, the distribution of stable and unstable regions corresponding to the memristor initial states is achieved, and the complex dynamical behaviors of the circuit depending on the circuit parameters and the memristor initial states are investigated. The theoretical analysis and numerical simulation results demonstrate that the proposed chaotic circuit with two memristors has an equilibrium set located on the plane constituted by the inner state variables of two memristors. The stability of the equilibrium set depends on both the circuit parameters and the initial states of the two memristors. Rich nonlinear dynamical phenomena, such as state transitions, transient hyperchaos and so on, are expected.展开更多
The aim of this work is to analyse the global dynamics of an extended mathematical model of Hepatitis C virus (HCV) infection in vivo with cellular proliferation, spontaneous cure and hepatocyte homeostasis. We firstl...The aim of this work is to analyse the global dynamics of an extended mathematical model of Hepatitis C virus (HCV) infection in vivo with cellular proliferation, spontaneous cure and hepatocyte homeostasis. We firstly prove the existence of local and global solutions of the model and establish some properties of this solution as positivity and asymptotic behaviour. Secondly we show, by the construction of appropriate Lyapunov functions, that the uninfected equilibrium and the unique infected equilibrium of the mathematical model of HCV are globally asymptotically stable respectively when the threshold number and when .展开更多
In this paper,as for the unmanned air vehicle(UAV)under external disturbance,an attainable-equilibrium-set-based safety fight envelope(SFE)calculation method is proposed,based on which a prescribed performance protect...In this paper,as for the unmanned air vehicle(UAV)under external disturbance,an attainable-equilibrium-set-based safety fight envelope(SFE)calculation method is proposed,based on which a prescribed performance protection control scheme is presented.Firstly,the existing definition of the SFE based on attainable equilibrium set(AES)is extended to make it consistent and suitable for the UAV system under disturbance.Secondly,a higher-order disturbance observer(HODO)is developed to estimate the disturbances and the disturbance estimation is applied in the computation of the SFE.Thirdly,by using the calculated SFE,a desired safety trajectory based on the time-varying safety margin function and first-order filter is developed to prevent the states of the UAV system from exceeding the SFE.Moreover,an SFE protection controller is proposed by combining the desired safety trajectory,backstepping method,HODO design,and prescribed performance(PP)control technique.In particular,the closed-loop system is established on the basis of disturbance estimation error,filter error,and tracking error.Finally,the stability of the closed-loop system is verified by the Lyapunov stability theory,and the simulations are presented to illustrate the effectiveness of the proposed control scheme.展开更多
Safety is regarded as the second basic need in Maslow’s hierarchy of needs(1943),and safety recognition and circumvention behaviour in the route-choice decision-making process should therefore be accommodated in netw...Safety is regarded as the second basic need in Maslow’s hierarchy of needs(1943),and safety recognition and circumvention behaviour in the route-choice decision-making process should therefore be accommodated in network-traffic equilibrium analysis frameworks.This paper proposes a framework by which crash frequency,forecasted using the safety-analysis method or compiled from historical data for intersections,is used to measure the safety consciousness of drivers.Drivers are then classified into different groups according to their acceptable-risk thresholds,and each group has its own route-choice set.Decision behaviour whereby drivers are willing to bear additional costs in order to circumvent travel risk is incorporated into the variational inequality model based on the user equilibrium in the perceived route-choice set(UE-PRCS),which is an extension of Wardrop’s first principle.The Frank–Wolfe algorithm,based on the convex combination method,is employed to obtain the solution.A small road network is used as a case study to illustrate the proposed framework,incorporating risk recognition and circumvention behaviour under different combinations of traffic demand and risk-sensitivity group ratio.The results show that the standard user equilibrium is a special case of the UE-PRCS,but that the UE traffic state is more common than the UE-PRCS under different parameters.展开更多
The quaternion Mandelbrot set is one of the most important sets in mathematics. In this paper we first give some properties of the quaternion algebra. Then, we introduce the quternion dynamical system. We are concerne...The quaternion Mandelbrot set is one of the most important sets in mathematics. In this paper we first give some properties of the quaternion algebra. Then, we introduce the quternion dynamical system. We are concerned with analytical and numerical investigation of the quaternion dynamical system.展开更多
We study the existence of competitive equilibria when the excess demand function fails to satisfy the standard boundary behavior. We introduce alternative boundary conditions and we examine their role in proving the e...We study the existence of competitive equilibria when the excess demand function fails to satisfy the standard boundary behavior. We introduce alternative boundary conditions and we examine their role in proving the existence of strictly positive solutions to a system of non-linear equations (competitive equilibium prices). In addition, we slightly generalize a well-known theorem on the existence of maximal elements, and we unveil the link between the hypothesis of our theorem and one of the boundary conditions introduced in this work.展开更多
A number of solution concepts of normal-form games have been proposed in the literature on subspaces of action profiles that have Nash type stability. While the literature mainly focuses oil the minimal of such stable...A number of solution concepts of normal-form games have been proposed in the literature on subspaces of action profiles that have Nash type stability. While the literature mainly focuses oil the minimal of such stable subspaces, this paper argues that non-minimal stable subspaces represent well the multi-agent situations to which neither Nash equilibrium nor rationalizability may be applied with satisfaction. As a theoretical support, the authors prove the optimal substructure of stable subspaces regarding the restriction of a game. It is further argued that the optimal substructure characterizes hierarchical diversity of coordination and interim phases in learning.展开更多
Generalized vectorial quasi-equilibrium problem and generalized set-valued quasi-equilibrium problem are introduced and the existence theorems of generalized vectorial quasi-equilihrium problem on W-space are obtained...Generalized vectorial quasi-equilibrium problem and generalized set-valued quasi-equilibrium problem are introduced and the existence theorems of generalized vectorial quasi-equilihrium problem on W-space are obtained. As corollaries, existence theorems of four kinds of quasi-equilibrium problem are obtained, and these results generalize and improve correspond results in [1-7] .展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 60971090)the Natural Science Foundations of Jiangsu Province, China (Grant No. BK2009105)
文摘Based on Chua’s chaotic oscillation circuit, a fifth-order chaotic circuit with two memristors is designed and its corresponding dimensionless mathematic model is established. By using conventional dynamical analysis methods, stability analysis of the equilibrium set of the circuit is performed, the distribution of stable and unstable regions corresponding to the memristor initial states is achieved, and the complex dynamical behaviors of the circuit depending on the circuit parameters and the memristor initial states are investigated. The theoretical analysis and numerical simulation results demonstrate that the proposed chaotic circuit with two memristors has an equilibrium set located on the plane constituted by the inner state variables of two memristors. The stability of the equilibrium set depends on both the circuit parameters and the initial states of the two memristors. Rich nonlinear dynamical phenomena, such as state transitions, transient hyperchaos and so on, are expected.
文摘The aim of this work is to analyse the global dynamics of an extended mathematical model of Hepatitis C virus (HCV) infection in vivo with cellular proliferation, spontaneous cure and hepatocyte homeostasis. We firstly prove the existence of local and global solutions of the model and establish some properties of this solution as positivity and asymptotic behaviour. Secondly we show, by the construction of appropriate Lyapunov functions, that the uninfected equilibrium and the unique infected equilibrium of the mathematical model of HCV are globally asymptotically stable respectively when the threshold number and when .
基金supported in part by the National Science Fund for Distinguished Young Scholars 61825302in part by the National Natural Science Foundation of China under Grant U2013201in part by the Key R&D projects(Social Development)in Jiangsu Province of China under Grant BE2020704.
文摘In this paper,as for the unmanned air vehicle(UAV)under external disturbance,an attainable-equilibrium-set-based safety fight envelope(SFE)calculation method is proposed,based on which a prescribed performance protection control scheme is presented.Firstly,the existing definition of the SFE based on attainable equilibrium set(AES)is extended to make it consistent and suitable for the UAV system under disturbance.Secondly,a higher-order disturbance observer(HODO)is developed to estimate the disturbances and the disturbance estimation is applied in the computation of the SFE.Thirdly,by using the calculated SFE,a desired safety trajectory based on the time-varying safety margin function and first-order filter is developed to prevent the states of the UAV system from exceeding the SFE.Moreover,an SFE protection controller is proposed by combining the desired safety trajectory,backstepping method,HODO design,and prescribed performance(PP)control technique.In particular,the closed-loop system is established on the basis of disturbance estimation error,filter error,and tracking error.Finally,the stability of the closed-loop system is verified by the Lyapunov stability theory,and the simulations are presented to illustrate the effectiveness of the proposed control scheme.
基金supported by National Social Science Foundation of China(14BTJ017).
文摘Safety is regarded as the second basic need in Maslow’s hierarchy of needs(1943),and safety recognition and circumvention behaviour in the route-choice decision-making process should therefore be accommodated in network-traffic equilibrium analysis frameworks.This paper proposes a framework by which crash frequency,forecasted using the safety-analysis method or compiled from historical data for intersections,is used to measure the safety consciousness of drivers.Drivers are then classified into different groups according to their acceptable-risk thresholds,and each group has its own route-choice set.Decision behaviour whereby drivers are willing to bear additional costs in order to circumvent travel risk is incorporated into the variational inequality model based on the user equilibrium in the perceived route-choice set(UE-PRCS),which is an extension of Wardrop’s first principle.The Frank–Wolfe algorithm,based on the convex combination method,is employed to obtain the solution.A small road network is used as a case study to illustrate the proposed framework,incorporating risk recognition and circumvention behaviour under different combinations of traffic demand and risk-sensitivity group ratio.The results show that the standard user equilibrium is a special case of the UE-PRCS,but that the UE traffic state is more common than the UE-PRCS under different parameters.
文摘The quaternion Mandelbrot set is one of the most important sets in mathematics. In this paper we first give some properties of the quaternion algebra. Then, we introduce the quternion dynamical system. We are concerned with analytical and numerical investigation of the quaternion dynamical system.
文摘We study the existence of competitive equilibria when the excess demand function fails to satisfy the standard boundary behavior. We introduce alternative boundary conditions and we examine their role in proving the existence of strictly positive solutions to a system of non-linear equations (competitive equilibium prices). In addition, we slightly generalize a well-known theorem on the existence of maximal elements, and we unveil the link between the hypothesis of our theorem and one of the boundary conditions introduced in this work.
文摘A number of solution concepts of normal-form games have been proposed in the literature on subspaces of action profiles that have Nash type stability. While the literature mainly focuses oil the minimal of such stable subspaces, this paper argues that non-minimal stable subspaces represent well the multi-agent situations to which neither Nash equilibrium nor rationalizability may be applied with satisfaction. As a theoretical support, the authors prove the optimal substructure of stable subspaces regarding the restriction of a game. It is further argued that the optimal substructure characterizes hierarchical diversity of coordination and interim phases in learning.
基金Supported by the Applied Basic Research Foundation of Chongqing city.
文摘Generalized vectorial quasi-equilibrium problem and generalized set-valued quasi-equilibrium problem are introduced and the existence theorems of generalized vectorial quasi-equilihrium problem on W-space are obtained. As corollaries, existence theorems of four kinds of quasi-equilibrium problem are obtained, and these results generalize and improve correspond results in [1-7] .
