Using the theory of existence of periodic solutions of Hamiltonian systems, it is shown that many periodic solutions of differential delay equations can be yielded from many families of periodic solutions of the coupl...Using the theory of existence of periodic solutions of Hamiltonian systems, it is shown that many periodic solutions of differential delay equations can be yielded from many families of periodic solutions of the coupled generalized Hamiltonian systems. Some sufficient conditions on the existence of periodic solutions of differential delay equations are obtained. As a corollary of our results, the conjecture of Kaplan-Yorke on the search for periodic solutions for certain special classes of scalar differential delay equations is shown to be true when f' (0) =ω> 0.展开更多
The authors establish the existence of nontrival periodic solntions of the asymptotically linear Hamiltonian systems in the general case that the asymptotic matrix may be degenerate and time-dependent.This is done by ...The authors establish the existence of nontrival periodic solntions of the asymptotically linear Hamiltonian systems in the general case that the asymptotic matrix may be degenerate and time-dependent.This is done by using the critical point theory,Galerkin approximation procedure and the Maslov-type index theory introduced and generalized by Conley,Zehnder and Long.展开更多
With the increasing railway vehicle speed, pantograph--catenary （PAC） system has become an important part as its incidents still stand among the prin- cipal causes of railway traffic interruption. Indeed, when a rai...With the increasing railway vehicle speed, pantograph--catenary （PAC） system has become an important part as its incidents still stand among the prin- cipal causes of railway traffic interruption. Indeed, when a rail vehicle moves, the pantograph should constantly press against the underside of the catenary. Nonetheless, it is difficult to get around the complexity of the physical interaction between the pantograph and the contact wire, which could deteriorate the quality of the electricity transfer. Thus, PAC system performances could dramati- cally be reduced because of bad current collection. Therefore, in this paper, we present an output feedback solution in order to design an active control of PAC system. The proposed solution is based on the backstepping control and an adaptive observer that estimates both the （unknown） catenary parameters and the system state. All synthesis steps are given and the closed-loop analysis shows asymptotic tracking behavior regardless of the time-vary- ing catenary stiffness. Furthermore, a numerical example shows that the PAC contact can be regulated with desired effect.展开更多
Considering a decomposition R2N=A⊕B of R2N , we prove in this work, the existence of at least (1+dimA) geometrically distinct periodic solutions for the first-order Hamiltonian system Jx'(t)+H'(t,x(t))+e(t)=0...Considering a decomposition R2N=A⊕B of R2N , we prove in this work, the existence of at least (1+dimA) geometrically distinct periodic solutions for the first-order Hamiltonian system Jx'(t)+H'(t,x(t))+e(t)=0 when the Hamiltonian H(t,u+v) is periodic in (t,u) and its growth at infinity in v is at most like or faster than |v|a, 0≤ae is a forcing term. For the proof, we use the Least Action Principle and a Generalized Saddle Point Theorem.展开更多
Due to its good potential for digital signal processing, discrete Gabor analysis has interested some mathematicians. This paper addresses Gabor systems on discrete periodic sets, which can model signals to appear peri...Due to its good potential for digital signal processing, discrete Gabor analysis has interested some mathematicians. This paper addresses Gabor systems on discrete periodic sets, which can model signals to appear periodically but intermittently. Complete Gabor systems and Gabor frames on discrete periodic sets are characterized; a sufficient and necessary condition on what periodic sets admit complete Gabor systems is obtained; this condition is also proved to be sufficient and necessary for the existence of sets E such that the Gabor systems generated by χE are tight frames on these periodic sets; our proof is constructive, and all tight frames of the above form with a special frame bound can be obtained by our method; periodic sets admitting Gabor Riesz bases are characterized; some examples are also provided to illustrate the general theory.展开更多
The sufficient condition for the existence of non constant periodic solutions of the following planar system with four delays are obtained:x [FK(W1*1。*3/4]′ 1(t)=-a 0x α 1(t)+a 1f 1(x 1(t-τ 1),x 2...The sufficient condition for the existence of non constant periodic solutions of the following planar system with four delays are obtained:x [FK(W1*1。*3/4]′ 1(t)=-a 0x α 1(t)+a 1f 1(x 1(t-τ 1),x 2(t-τ 2)), x [FK(W1*1。*3/4]′ 2(t)=-b 0x α 2(t)+b 1f 2(x 1(t-τ 3),x 2(t-τ 4)).This approach is based on the continuation theorem of the coincidence degree, and the a priori estimate of periodic solutions.展开更多
For linear difference systems, a rather general result on the existence of almost periodic solutions is established, which also gives the explicit expression of the almost periodic solution in terms of the coefficient...For linear difference systems, a rather general result on the existence of almost periodic solutions is established, which also gives the explicit expression of the almost periodic solution in terms of the coefficient matrix and the nonhomogeneous term. The obtained result confirms not only the existence, but also the uniqueness as well as the uniform asymptotic stability of the almost periodic solution. As an application, a criterion on the existence of almost periodic solutions of the second order difference equations is derived.展开更多
We study the time evolution of electron wavepacket in the coupled two-dimensional(2D)lattices with mirror symmetry,utilizing the tight-binding Hamiltonian framework.We show analytically that the wavepacket of an elect...We study the time evolution of electron wavepacket in the coupled two-dimensional(2D)lattices with mirror symmetry,utilizing the tight-binding Hamiltonian framework.We show analytically that the wavepacket of an electron initially located on one atomic layer in the coupled 2D square lattices exhibits a periodic oscillation in both the transverse and longitudinal directions.The frequency of this oscillation is determined by the strength of the interlayer hopping.Additionally,we provide numerical evidence that a damped periodic oscillation occurs in the coupled 2D disordered lattices with degree of disorderW,with the decay time being inversely proportional to the square ofW and the frequency change being proportional to the square of W,which is similar to the case in the coupled 1D disordered lattices.Our numerical results further confirm that the periodic and damped periodic electron oscillations are universal,independent of lattice geometry,as demonstrated in AA-stacked bilayer and tri-layer graphene systems.Unlike the Bloch oscillation driven by electric fields,the periodic oscillation induced by interlayer coupling does not require the application of an electric field,has an ultrafast periodicity much shorter than the electron decoherence time in real materials,and can be tuned by adjusting the interlayer coupling.Our findings pave the way for future observation of periodic electron oscillation in material systems at the atomic scale.展开更多
The parameter embedding method is applied for numerically solving the perturbed conservative systems. By means of Newtonian iteration, a simple algorithm has been constructed. Finally, the convergence of the iteration...The parameter embedding method is applied for numerically solving the perturbed conservative systems. By means of Newtonian iteration, a simple algorithm has been constructed. Finally, the convergence of the iteration is proved.展开更多
In this paper, under a similar but stronger condition than that of Ambrosetti and Rabinowitz we find a T-periodic solution of the autonomous superquadratic second order Hamiltonian system with even potential for any T...In this paper, under a similar but stronger condition than that of Ambrosetti and Rabinowitz we find a T-periodic solution of the autonomous superquadratic second order Hamiltonian system with even potential for any T 〉 0; moreover, such a solution has T as its minimal period.展开更多
In this paper, using the KAM theorem of reversible systems, we obtain the boundednessof solutions, the existence of quasi-periodic solutions and subharmonic solutions for the non-linear differential equations of the s...In this paper, using the KAM theorem of reversible systems, we obtain the boundednessof solutions, the existence of quasi-periodic solutions and subharmonic solutions for the non-linear differential equations of the second order which is neither conservative nor dissipative.展开更多
This paper presents two contributions to the stability analysis of periodic systems modeled by a Hill equation: The first is a new method for the computation of the Arnold Tongues associated to a given Hill equation w...This paper presents two contributions to the stability analysis of periodic systems modeled by a Hill equation: The first is a new method for the computation of the Arnold Tongues associated to a given Hill equation which is based on the discretization of the latter. Using the proposed method, a vibrational stabilization is performed by a change in the periodic function which guarantees stability, given that the original equation has unbounded solutions. The results are illustrated by some examples.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 19731003)Science Foundation of Yunnan Province.
文摘Using the theory of existence of periodic solutions of Hamiltonian systems, it is shown that many periodic solutions of differential delay equations can be yielded from many families of periodic solutions of the coupled generalized Hamiltonian systems. Some sufficient conditions on the existence of periodic solutions of differential delay equations are obtained. As a corollary of our results, the conjecture of Kaplan-Yorke on the search for periodic solutions for certain special classes of scalar differential delay equations is shown to be true when f' (0) =ω> 0.
文摘The authors establish the existence of nontrival periodic solntions of the asymptotically linear Hamiltonian systems in the general case that the asymptotic matrix may be degenerate and time-dependent.This is done by using the critical point theory,Galerkin approximation procedure and the Maslov-type index theory introduced and generalized by Conley,Zehnder and Long.
文摘With the increasing railway vehicle speed, pantograph--catenary （PAC） system has become an important part as its incidents still stand among the prin- cipal causes of railway traffic interruption. Indeed, when a rail vehicle moves, the pantograph should constantly press against the underside of the catenary. Nonetheless, it is difficult to get around the complexity of the physical interaction between the pantograph and the contact wire, which could deteriorate the quality of the electricity transfer. Thus, PAC system performances could dramati- cally be reduced because of bad current collection. Therefore, in this paper, we present an output feedback solution in order to design an active control of PAC system. The proposed solution is based on the backstepping control and an adaptive observer that estimates both the （unknown） catenary parameters and the system state. All synthesis steps are given and the closed-loop analysis shows asymptotic tracking behavior regardless of the time-vary- ing catenary stiffness. Furthermore, a numerical example shows that the PAC contact can be regulated with desired effect.
文摘Considering a decomposition R2N=A⊕B of R2N , we prove in this work, the existence of at least (1+dimA) geometrically distinct periodic solutions for the first-order Hamiltonian system Jx'(t)+H'(t,x(t))+e(t)=0 when the Hamiltonian H(t,u+v) is periodic in (t,u) and its growth at infinity in v is at most like or faster than |v|a, 0≤ae is a forcing term. For the proof, we use the Least Action Principle and a Generalized Saddle Point Theorem.
基金supported by National Natural Science Foundation of China (Grant No. 10671008)Beijing Natural Science Foundation (Grant No. 1092001)PHR (IHLB) and the project sponsored by SRF for ROCS,SEM of China
文摘Due to its good potential for digital signal processing, discrete Gabor analysis has interested some mathematicians. This paper addresses Gabor systems on discrete periodic sets, which can model signals to appear periodically but intermittently. Complete Gabor systems and Gabor frames on discrete periodic sets are characterized; a sufficient and necessary condition on what periodic sets admit complete Gabor systems is obtained; this condition is also proved to be sufficient and necessary for the existence of sets E such that the Gabor systems generated by χE are tight frames on these periodic sets; our proof is constructive, and all tight frames of the above form with a special frame bound can be obtained by our method; periodic sets admitting Gabor Riesz bases are characterized; some examples are also provided to illustrate the general theory.
文摘The sufficient condition for the existence of non constant periodic solutions of the following planar system with four delays are obtained:x [FK(W1*1。*3/4]′ 1(t)=-a 0x α 1(t)+a 1f 1(x 1(t-τ 1),x 2(t-τ 2)), x [FK(W1*1。*3/4]′ 2(t)=-b 0x α 2(t)+b 1f 2(x 1(t-τ 3),x 2(t-τ 4)).This approach is based on the continuation theorem of the coincidence degree, and the a priori estimate of periodic solutions.
文摘For linear difference systems, a rather general result on the existence of almost periodic solutions is established, which also gives the explicit expression of the almost periodic solution in terms of the coefficient matrix and the nonhomogeneous term. The obtained result confirms not only the existence, but also the uniqueness as well as the uniform asymptotic stability of the almost periodic solution. As an application, a criterion on the existence of almost periodic solutions of the second order difference equations is derived.
基金Project supported by the National Natural Science Foundation of China(Grant No.11874316)the National Basic Research Program of China(Grant No.2015CB921103)the International Visiting Faculty Program of Hunan Provincial Government,China.
文摘We study the time evolution of electron wavepacket in the coupled two-dimensional(2D)lattices with mirror symmetry,utilizing the tight-binding Hamiltonian framework.We show analytically that the wavepacket of an electron initially located on one atomic layer in the coupled 2D square lattices exhibits a periodic oscillation in both the transverse and longitudinal directions.The frequency of this oscillation is determined by the strength of the interlayer hopping.Additionally,we provide numerical evidence that a damped periodic oscillation occurs in the coupled 2D disordered lattices with degree of disorderW,with the decay time being inversely proportional to the square ofW and the frequency change being proportional to the square of W,which is similar to the case in the coupled 1D disordered lattices.Our numerical results further confirm that the periodic and damped periodic electron oscillations are universal,independent of lattice geometry,as demonstrated in AA-stacked bilayer and tri-layer graphene systems.Unlike the Bloch oscillation driven by electric fields,the periodic oscillation induced by interlayer coupling does not require the application of an electric field,has an ultrafast periodicity much shorter than the electron decoherence time in real materials,and can be tuned by adjusting the interlayer coupling.Our findings pave the way for future observation of periodic electron oscillation in material systems at the atomic scale.
文摘The parameter embedding method is applied for numerically solving the perturbed conservative systems. By means of Newtonian iteration, a simple algorithm has been constructed. Finally, the convergence of the iteration is proved.
基金supported by the 973 Project of Science and Technology
文摘In this paper, under a similar but stronger condition than that of Ambrosetti and Rabinowitz we find a T-periodic solution of the autonomous superquadratic second order Hamiltonian system with even potential for any T 〉 0; moreover, such a solution has T as its minimal period.
文摘In this paper, using the KAM theorem of reversible systems, we obtain the boundednessof solutions, the existence of quasi-periodic solutions and subharmonic solutions for the non-linear differential equations of the second order which is neither conservative nor dissipative.
文摘This paper presents two contributions to the stability analysis of periodic systems modeled by a Hill equation: The first is a new method for the computation of the Arnold Tongues associated to a given Hill equation which is based on the discretization of the latter. Using the proposed method, a vibrational stabilization is performed by a change in the periodic function which guarantees stability, given that the original equation has unbounded solutions. The results are illustrated by some examples.
