The state space representation of the Bezout identity for generalized systems proposed by (Wang and Balas, 1989) is discussed again. A more concise way of description and proof is presented and the physical signific...The state space representation of the Bezout identity for generalized systems proposed by (Wang and Balas, 1989) is discussed again. A more concise way of description and proof is presented and the physical significance of the result in is also analyzed. Thus, our work is of independent interest.展开更多
In this paper, we introduce a generalized system (for short, GS) in real Banach spaces. Using Brouwer’s fixed point theorem, we establish some existence theorems for the generalized system without monotonicity. Furth...In this paper, we introduce a generalized system (for short, GS) in real Banach spaces. Using Brouwer’s fixed point theorem, we establish some existence theorems for the generalized system without monotonicity. Further, we extend the concept of C-strong pseudomonotonicity and extend Minty’s lemma for the generalized system. And using the Minty lemma and KKM-Fan lemma, we establish an existence theorem for the generalized system with monotonicity in real reflexive Banach spaces. As the continuation of existing studies, our paper present a series of extended results based on existing corresponding results.展开更多
Fractional calculus is widely used to deal with nonconservative dynamics because of its memorability and non-local properties.In this paper,the Herglotz principle with generalized operators is discussed,and the Herglo...Fractional calculus is widely used to deal with nonconservative dynamics because of its memorability and non-local properties.In this paper,the Herglotz principle with generalized operators is discussed,and the Herglotz type equations for nonholonomic systems are established.Then,the Noether symmetries are studied,and the conserved quantities are obtained.The results are extended to nonholonomic canonical systems,and the Herglotz type canonical equations and the Noether theorems are obtained.Two examples are provided to demonstrate the validity of the methods and results.展开更多
Recently, during the investigations on planetary oceans, Hirota-Satsuma-Ito-type models have been developed. In this paper, for a(2+1)-dimensional generalized variable-coefficient Hirota-Satsuma-Ito system describing ...Recently, during the investigations on planetary oceans, Hirota-Satsuma-Ito-type models have been developed. In this paper, for a(2+1)-dimensional generalized variable-coefficient Hirota-Satsuma-Ito system describing the fluid dynamics of shallow-water waves in an open ocean, non-characteristic movable singular manifold and symbolic computation enable an oceanic auto-B?cklund transformation with three sets of the oceanic solitonic solutions. The results rely on the oceanic variable coefficients in that system. Future oceanic observations might detect some nonlinear features predicted in this paper, and relevant oceanographic insights might be expected.展开更多
In this paper,the synchronizable system by groups and the generalized synchronizable system are studied for a coupled system of wave equations.Moreover,situations possessing different groupings are also discussed.
To study the Poisson theory of the generalized Birkhoff systems, the Lie algebra and the Poisson brackets were used to establish the Poisson theorem. The generalized Poisson condition for the first integral and the ge...To study the Poisson theory of the generalized Birkhoff systems, the Lie algebra and the Poisson brackets were used to establish the Poisson theorem. The generalized Poisson condition for the first integral and the generalized Poisson theorem of the generalized Birkhoff systems are obtained. An example is given to illustrate the application of the result.展开更多
Three kinds of symmetries and their corresponding conserved quantities of a generalized Birkhoffian system are studied. First, by using the invariance of the Pfaffian action under the infinitesimal transformations, th...Three kinds of symmetries and their corresponding conserved quantities of a generalized Birkhoffian system are studied. First, by using the invariance of the Pfaffian action under the infinitesimal transformations, the Noether theory of the generalized Birkhoffian system is established. Secondly, on the basis of the invariance of differential equations under infinitesimal transformations, the definition and the criterion of the Lie symmetry of the generalized Birkhoffian system are established, and the Hojman conserved quantity directly derived from the Lie symmetry of the system is given. Finally, by using the invariance that the dynamical functions in the differential equations of the motion of mechanical systems still satisfy the equations after undergoing the infinitesimal transformations, the definition and the criterion of the Mei symmetry of the generalized Birkhoffian system are presented, and the Mei conserved quantity directly derived from the Mei symmetry of the system is obtained. Some examples are given to illustrate the application of the results.展开更多
To study the application of the generalized predictive adaptive control algorithm in missile control system, the algorithm is presented based on the recursive least square estimation, and a controller of the pitch c...To study the application of the generalized predictive adaptive control algorithm in missile control system, the algorithm is presented based on the recursive least square estimation, and a controller of the pitch channel of a missile is designed by using this algorithm. The simulations verify that the designed controller can meet the demands of the task well.展开更多
Abstract The generalized system function, H（s）, directly associated with the radiated or scattered fields is presented to effectively analyze the special resonant behavior of electromagnetic open systems in this pap...Abstract The generalized system function, H（s）, directly associated with the radiated or scattered fields is presented to effectively analyze the special resonant behavior of electromagnetic open systems in this paper, which is adaptively constructed by using the model-based parameter estimation （MBPE） technique in the complex frequency domain. By analyzing the characteristics of complex zeros, poles and residues of H（s） in a finite operational frequency band, we can effectively determine resonant frequencies and resonant intensity of electromagnetic open systems. It is known that an analysis of Q-factor of antenna and scattering systems has been an interesting and challenging problem. Based on H（s） and the complex frequency w theories, a complex frequency method for Q-factor of electromagnetic open systems is presented in this paper. Some examples of the practical antenna arrays are given to illustrate the applications and validity of the generalized system function theory proposed by this paper.展开更多
The composite channel models of the generalized distributed antenna system （GDAS） such as Rayleigh-lognormal fading are studied. Then comparisons are performed between the GDAS and the traditional multiple-input mul...The composite channel models of the generalized distributed antenna system （GDAS） such as Rayleigh-lognormal fading are studied. Then comparisons are performed between the GDAS and the traditional multiple-input multiple-output （MIMO） system to analyze the ergodic capacity of the GDAS and make conclusions that it is impossible to achieve an analytical expression for the ergodic capacity of the GDAS. Moreover, in order to evaluate the performance of the ergodic capacity of the GDAS conveniently, the analytical lower bound and upper bound of the ergodic capacity of the GDAS are derived by using the results from multivariate statistics and matrix inequalities, under the scenarios of Rayleigh-lognormal fading and equal power allocation scheme at transmitter. Finally, the analytical bounds are verified by comparisons with the numerical results.展开更多
In this paper, a learning control approach is applied to the generalized projective synchronisation （GPS） of different chaotic systems with unknown periodically time-varying parameters. Using the Lyapunov--Krasovski...In this paper, a learning control approach is applied to the generalized projective synchronisation （GPS） of different chaotic systems with unknown periodically time-varying parameters. Using the Lyapunov--Krasovskii functional stability theory, a differential-difference mixed parametric learning law and an adaptive learning control law are constructed to make the states of two different chaotic systems asymptotically synchronised. The scheme is successfully applied to the generalized projective synchronisation between the Lorenz system and Chen system. Moreover, numerical simulations results are used to verify the effectiveness of the proposed scheme.展开更多
The system described by the generalized Birkhoff equations is called a generalized Birkhoffian system. In this paper, the condition under which the generalized Birkhoffian system can be a gradient system is given. The...The system described by the generalized Birkhoff equations is called a generalized Birkhoffian system. In this paper, the condition under which the generalized Birkhoffian system can be a gradient system is given. The stability of equilibrium of the generalized Birkhoffian system is discussed by using the properties of the gradient system. When there is a parameter in the equations, its influences on the stability and the bifurcation problem of the system are considered.展开更多
In this paper is investigated the generalized projective synchronization of a class of chaotic （or hyperchaotic） systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive...In this paper is investigated the generalized projective synchronization of a class of chaotic （or hyperchaotic） systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive technique, the globally generalized projective synchronization of two identical chaotic （hyperchaotic） systems is achieved by designing a novel nonlinear controller. Furthermore, the parameter identification is realized simultaneously. A sufficient condition for the globally projective synchronization is obtained. Finally, by taking the hyperchaotic L system as example, some numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed technique.展开更多
A more general form of projective synchronization, so called linear generalized synchronization （LGS） is proposed, which includes the generalized projective synchronization （GPS） and the hybrid projective synchron...A more general form of projective synchronization, so called linear generalized synchronization （LGS） is proposed, which includes the generalized projective synchronization （GPS） and the hybrid projective synchronization （HPS） as its special cases, Based on the adaptive technique and Lyapunov stability theory, a general method for achieving the LGS between two chaotic or hyperehaotic systems with uncertain parameters in any scaling matrix is presented. Some numerical simulations are provided to show the effectiveness and feasibility of the proposed synchronization method.展开更多
The skew-gradient representation of a generalized Birkhoffian system is studied. A condition under which the generalized Birkhoffian system can be considered as a skew-gradient system is obtained. The properties of th...The skew-gradient representation of a generalized Birkhoffian system is studied. A condition under which the generalized Birkhoffian system can be considered as a skew-gradient system is obtained. The properties of the skew-gradient system are used to study the properties, especially the stability, of the generalized Birkhoffian system. Some examples are given to illustrate the application of the result.展开更多
The theory of time scales,which unifies continuous and discrete analysis,provides a powerful mathematical tool for the study of complex dynamic systems.It enables us to understand more clearly the essential problems o...The theory of time scales,which unifies continuous and discrete analysis,provides a powerful mathematical tool for the study of complex dynamic systems.It enables us to understand more clearly the essential problems of continuous systems and discrete systems as well as other complex systems.In this paper,the theory of generalized canonical transformation for second-order Birkhoffian systems on time scales is proposed and studied,which extends the canonical transformation theory of Hamilton canonical equations.First,the condition of generalized canonical transformation for the second-order Birkhoffian system on time scales is established.Second,based on this condition,six basic forms of generalized canonical transformation for the second-order Birkhoffian system on time scales are given.Also,the relationships between new variables and old variables for each of these cases are derived.In the end,an example is given to show the application of the results.展开更多
By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equi...By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equilibrium existence theorems, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces. These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure.展开更多
The perturbations to symmetries and adiabatic invariants for nonconservative systems of generalized classical mechanics axe studied. The exact inwriant in the form of Hojman from a particular Lie symmetry for an undis...The perturbations to symmetries and adiabatic invariants for nonconservative systems of generalized classical mechanics axe studied. The exact inwriant in the form of Hojman from a particular Lie symmetry for an undisturbed system of generalized mechanics is given. Based on the concept of high-order adiabatic invaxiant in generalized mechanics, the perturbation to Lie symmetry for the system under the action of small disturbance is investigated, and a new adiabatic invaxiant for the nonconservative system of generalized classical mechanics is obtained, which can be called the Hojman adiabatic invaxiant. An example is also given to illustrate the application of the results.展开更多
Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the general...Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the generalized BirkhoiYian system and two propositions on the stability of the manifolds of equilibrium states of the system are obtained. An example is given to illustrate the application of the results.展开更多
Based on the invariance of differential equations under infinitesimal transformations of group, Lie symmetries, exact invariants, perturbation to the symmetries and adiabatic invariants in form of non-Noether for a La...Based on the invariance of differential equations under infinitesimal transformations of group, Lie symmetries, exact invariants, perturbation to the symmetries and adiabatic invariants in form of non-Noether for a Lagrange system are presented. Firstly, the exact invariants of generalized Hojman type led directly by Lie symmetries for a Lagrange system without perturbations are given. Then, on the basis of the concepts of Lie symmetries and higher order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for the system with the action of small disturbance is investigated, the adiabatic invariants of generalized Hojman type for the system are directly obtained, the conditions for existence of the adiabatic invariants and their forms are proved. Finally an example is presented to illustrate these results.展开更多
文摘The state space representation of the Bezout identity for generalized systems proposed by (Wang and Balas, 1989) is discussed again. A more concise way of description and proof is presented and the physical significance of the result in is also analyzed. Thus, our work is of independent interest.
文摘In this paper, we introduce a generalized system (for short, GS) in real Banach spaces. Using Brouwer’s fixed point theorem, we establish some existence theorems for the generalized system without monotonicity. Further, we extend the concept of C-strong pseudomonotonicity and extend Minty’s lemma for the generalized system. And using the Minty lemma and KKM-Fan lemma, we establish an existence theorem for the generalized system with monotonicity in real reflexive Banach spaces. As the continuation of existing studies, our paper present a series of extended results based on existing corresponding results.
基金supported by the National Natural Science Foundation of China(Grant No.12272248)the Postgraduate Research and Practice Innovation Program of Jiangsu Province of China(Grant No.KYCX23_3296).
文摘Fractional calculus is widely used to deal with nonconservative dynamics because of its memorability and non-local properties.In this paper,the Herglotz principle with generalized operators is discussed,and the Herglotz type equations for nonholonomic systems are established.Then,the Noether symmetries are studied,and the conserved quantities are obtained.The results are extended to nonholonomic canonical systems,and the Herglotz type canonical equations and the Noether theorems are obtained.Two examples are provided to demonstrate the validity of the methods and results.
基金financially supported by the Scientific Research Foundation of North China University of Technology (Grant Nos.11005136024XN147-87 and 110051360024XN151-86)。
文摘Recently, during the investigations on planetary oceans, Hirota-Satsuma-Ito-type models have been developed. In this paper, for a(2+1)-dimensional generalized variable-coefficient Hirota-Satsuma-Ito system describing the fluid dynamics of shallow-water waves in an open ocean, non-characteristic movable singular manifold and symbolic computation enable an oceanic auto-B?cklund transformation with three sets of the oceanic solitonic solutions. The results rely on the oceanic variable coefficients in that system. Future oceanic observations might detect some nonlinear features predicted in this paper, and relevant oceanographic insights might be expected.
基金Supported by the National Natural Science Foundation of China(12301577)Sichuan Science and Technology Program(2023NSFSC1346).
文摘In this paper,the synchronizable system by groups and the generalized synchronizable system are studied for a coupled system of wave equations.Moreover,situations possessing different groupings are also discussed.
文摘To study the Poisson theory of the generalized Birkhoff systems, the Lie algebra and the Poisson brackets were used to establish the Poisson theorem. The generalized Poisson condition for the first integral and the generalized Poisson theorem of the generalized Birkhoff systems are obtained. An example is given to illustrate the application of the result.
基金The National Natural Science Foundation of China(No.10972151)the Natural Science Foundation of Higher Education Institution of Jiangsu Province of China (No.08KJB130002)
文摘Three kinds of symmetries and their corresponding conserved quantities of a generalized Birkhoffian system are studied. First, by using the invariance of the Pfaffian action under the infinitesimal transformations, the Noether theory of the generalized Birkhoffian system is established. Secondly, on the basis of the invariance of differential equations under infinitesimal transformations, the definition and the criterion of the Lie symmetry of the generalized Birkhoffian system are established, and the Hojman conserved quantity directly derived from the Lie symmetry of the system is given. Finally, by using the invariance that the dynamical functions in the differential equations of the motion of mechanical systems still satisfy the equations after undergoing the infinitesimal transformations, the definition and the criterion of the Mei symmetry of the generalized Birkhoffian system are presented, and the Mei conserved quantity directly derived from the Mei symmetry of the system is obtained. Some examples are given to illustrate the application of the results.
文摘To study the application of the generalized predictive adaptive control algorithm in missile control system, the algorithm is presented based on the recursive least square estimation, and a controller of the pitch channel of a missile is designed by using this algorithm. The simulations verify that the designed controller can meet the demands of the task well.
文摘Abstract The generalized system function, H（s）, directly associated with the radiated or scattered fields is presented to effectively analyze the special resonant behavior of electromagnetic open systems in this paper, which is adaptively constructed by using the model-based parameter estimation （MBPE） technique in the complex frequency domain. By analyzing the characteristics of complex zeros, poles and residues of H（s） in a finite operational frequency band, we can effectively determine resonant frequencies and resonant intensity of electromagnetic open systems. It is known that an analysis of Q-factor of antenna and scattering systems has been an interesting and challenging problem. Based on H（s） and the complex frequency w theories, a complex frequency method for Q-factor of electromagnetic open systems is presented in this paper. Some examples of the practical antenna arrays are given to illustrate the applications and validity of the generalized system function theory proposed by this paper.
基金Foundation item:The National Natural Science Foundation of China(No.60496311)
文摘The composite channel models of the generalized distributed antenna system （GDAS） such as Rayleigh-lognormal fading are studied. Then comparisons are performed between the GDAS and the traditional multiple-input multiple-output （MIMO） system to analyze the ergodic capacity of the GDAS and make conclusions that it is impossible to achieve an analytical expression for the ergodic capacity of the GDAS. Moreover, in order to evaluate the performance of the ergodic capacity of the GDAS conveniently, the analytical lower bound and upper bound of the ergodic capacity of the GDAS are derived by using the results from multivariate statistics and matrix inequalities, under the scenarios of Rayleigh-lognormal fading and equal power allocation scheme at transmitter. Finally, the analytical bounds are verified by comparisons with the numerical results.
基金supported by the National Natural Science Foundation of China (Grant No. 60374015)
文摘In this paper, a learning control approach is applied to the generalized projective synchronisation （GPS） of different chaotic systems with unknown periodically time-varying parameters. Using the Lyapunov--Krasovskii functional stability theory, a differential-difference mixed parametric learning law and an adaptive learning control law are constructed to make the states of two different chaotic systems asymptotically synchronised. The scheme is successfully applied to the generalized projective synchronisation between the Lorenz system and Chen system. Moreover, numerical simulations results are used to verify the effectiveness of the proposed scheme.
基金supported by the National Natural Science Foundation of China(Grant No.11272050)
文摘The system described by the generalized Birkhoff equations is called a generalized Birkhoffian system. In this paper, the condition under which the generalized Birkhoffian system can be a gradient system is given. The stability of equilibrium of the generalized Birkhoffian system is discussed by using the properties of the gradient system. When there is a parameter in the equations, its influences on the stability and the bifurcation problem of the system are considered.
基金Project supported by the National Natural Science Foundation of China （Grant No 60574045） and partly by Foundation of Guangxi Department of Education, China （Grant No （2006）26-118）.
文摘In this paper is investigated the generalized projective synchronization of a class of chaotic （or hyperchaotic） systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive technique, the globally generalized projective synchronization of two identical chaotic （hyperchaotic） systems is achieved by designing a novel nonlinear controller. Furthermore, the parameter identification is realized simultaneously. A sufficient condition for the globally projective synchronization is obtained. Finally, by taking the hyperchaotic L system as example, some numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed technique.
基金the National Natural Science Foundation of China (60574045 10661006).
文摘A more general form of projective synchronization, so called linear generalized synchronization （LGS） is proposed, which includes the generalized projective synchronization （GPS） and the hybrid projective synchronization （HPS） as its special cases, Based on the adaptive technique and Lyapunov stability theory, a general method for achieving the LGS between two chaotic or hyperehaotic systems with uncertain parameters in any scaling matrix is presented. Some numerical simulations are provided to show the effectiveness and feasibility of the proposed synchronization method.
基金Project supported by the National Natural Science Foundation of China(Grant No.11272050)
文摘The skew-gradient representation of a generalized Birkhoffian system is studied. A condition under which the generalized Birkhoffian system can be considered as a skew-gradient system is obtained. The properties of the skew-gradient system are used to study the properties, especially the stability, of the generalized Birkhoffian system. Some examples are given to illustrate the application of the result.
基金supported by the National Natural Science Foundation of China(Grants 11972241 and 11572212)
文摘The theory of time scales,which unifies continuous and discrete analysis,provides a powerful mathematical tool for the study of complex dynamic systems.It enables us to understand more clearly the essential problems of continuous systems and discrete systems as well as other complex systems.In this paper,the theory of generalized canonical transformation for second-order Birkhoffian systems on time scales is proposed and studied,which extends the canonical transformation theory of Hamilton canonical equations.First,the condition of generalized canonical transformation for the second-order Birkhoffian system on time scales is established.Second,based on this condition,six basic forms of generalized canonical transformation for the second-order Birkhoffian system on time scales are given.Also,the relationships between new variables and old variables for each of these cases are derived.In the end,an example is given to show the application of the results.
基金This project was supported by the NSF of Sichuan Education of China(2003A081)and SZD0406
文摘By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equilibrium existence theorems, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces. These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure.
基金Project supported by the Natural Science Foundation of High Education of Jiangsu Province, China （Grant No 04KJA130135）.
文摘The perturbations to symmetries and adiabatic invariants for nonconservative systems of generalized classical mechanics axe studied. The exact inwriant in the form of Hojman from a particular Lie symmetry for an undisturbed system of generalized mechanics is given. Based on the concept of high-order adiabatic invaxiant in generalized mechanics, the perturbation to Lie symmetry for the system under the action of small disturbance is investigated, and a new adiabatic invaxiant for the nonconservative system of generalized classical mechanics is obtained, which can be called the Hojman adiabatic invaxiant. An example is also given to illustrate the application of the results.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10772025,10932002 and 10972127)the Natural Science Foundation of Henan Province,China(Grant No.102300410144)the Beijing Municipal Key Disciplines Fund for General Mechanics and Foundation of Mechanics,China
文摘Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the generalized BirkhoiYian system and two propositions on the stability of the manifolds of equilibrium states of the system are obtained. An example is given to illustrate the application of the results.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10472040 and 10372053）, the Natural Science Foundation of Hunan Province, China （Grant No 03JJY3005）, the Natural Science Foundation of Henan Province, China （Grant No 0311010900）, the 0utstanding Young Talents Training Fund of Liaoning Province, China （Grant No 3040005） and the Foundation of Young Key Member of the teachers in Institutions of Higher Learning of Henan Province of China.
文摘Based on the invariance of differential equations under infinitesimal transformations of group, Lie symmetries, exact invariants, perturbation to the symmetries and adiabatic invariants in form of non-Noether for a Lagrange system are presented. Firstly, the exact invariants of generalized Hojman type led directly by Lie symmetries for a Lagrange system without perturbations are given. Then, on the basis of the concepts of Lie symmetries and higher order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for the system with the action of small disturbance is investigated, the adiabatic invariants of generalized Hojman type for the system are directly obtained, the conditions for existence of the adiabatic invariants and their forms are proved. Finally an example is presented to illustrate these results.
