To study controlled evolution of nonautonomous matter-wave breathers and rogue waves in spinor Bose–Einstein condensates with spatiotemporal modulation,we focus on a system of three coupled Gross–Pitaevskii equation...To study controlled evolution of nonautonomous matter-wave breathers and rogue waves in spinor Bose–Einstein condensates with spatiotemporal modulation,we focus on a system of three coupled Gross–Pitaevskii equations with spacetime-dependent external potentials and temporally modulated gain-loss distributions.With different external potentials and gain-loss distributions,various solutions for controlled nonautonomous matterwave breathers and rogue waves are derived by the Darboux transformation method,such as breathers and rogue waves on arched and constant backgrounds which have the periodic and parabolic trajectories.Effects of the gain-loss distribution and linear potential on the breathers and rogue waves are studied.Nonautonomous two-breathers on the arched and constant backgrounds are also derived.展开更多
Let(X,φ) be a nonautonomous dynamical system.In this paper,we introduce the notions of packing topological entropy and measure-theoretical upper entropy for nonautonomous dynamical systems.Moreover,we establish the v...Let(X,φ) be a nonautonomous dynamical system.In this paper,we introduce the notions of packing topological entropy and measure-theoretical upper entropy for nonautonomous dynamical systems.Moreover,we establish the variational principle between the packing topological entropy and the measure-theoretical upper entropy.展开更多
In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive relea...In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive release and general nonlinear incidence rate and investigate dynamical behaviors of the model. Under the reasonable assumptions, the sufficient conditions which guarantee the globally attractive of the disease-free periodic solution and the permanence of the infected fish are established, that is, the infected fish dies out if , whereas the disease persists if . To substantiate our theoretical results, extensive numerical simulations are performed for a hypothetical set of parameter values.展开更多
In this paper the stability of nonlinear nonautonomous systems under the frequently-acting perturbation is studied.This study is a forward development of the study of thestability in the Liapunov sense;furthermore,it ...In this paper the stability of nonlinear nonautonomous systems under the frequently-acting perturbation is studied.This study is a forward development of the study of thestability in the Liapunov sense;furthermore,it is of significance in practice sinceperturbations are often not single in the time domain.Malk in proved a general theoremabout thesubject.To apply the theorem,however,the user has to construct a Liapunovfunction which satisfies specified conditions and it is difficult to find such a function fornonlinear nonautonomous systems.In the light of the principle of Liapunov’s indirectmethod,which is an effective method to decide the stability of nonlinear systems in theLiapunov sense,the authors have achieved several important conclusions expressed in theform of theorems to determine the stability of nonlinear nonautonomous systems under thefrequently-acting perturbation.展开更多
The long_time behaviour of a two_dimensional nonautonomous nonlinear Schrdinger equation is considered. The existence of uniform attractor is proved and the upper bound of the uniform attractor’s Hausdorff dimension ...The long_time behaviour of a two_dimensional nonautonomous nonlinear Schrdinger equation is considered. The existence of uniform attractor is proved and the upper bound of the uniform attractor’s Hausdorff dimension is given.展开更多
The necessary and sufficient condition of the stability of linear nonautonomous system under the frequently-acting perturbation has been given and proved on the basis of[1]and[2],and the theorem of the equivalence on ...The necessary and sufficient condition of the stability of linear nonautonomous system under the frequently-acting perturbation has been given and proved on the basis of[1]and[2],and the theorem of the equivalence on the uniform and asymptotical stability in the sense of Liapunov and the stability under the frequently-acting perturbation of linear nonautonomous system has been given in this paper.Besides,the analysis of the dynamic stability of robot has been presented by applying the theorem in this paper,which is closer to reality.展开更多
In this paper, the long time behavior of nonautonomous infinite dimensional dynamical systems is studied, A family of convergent approximate inertial manifolds for a class of evolution equations has been constructed w...In this paper, the long time behavior of nonautonomous infinite dimensional dynamical systems is studied, A family of convergent approximate inertial manifolds for a class of evolution equations has been constructed when the spectral gap condition is satisfied.展开更多
In this paper, the long time behavior of nonautonomous infinite dimensional dynamical systems is discussed. Under the spectral gap condition. It is proved that there exist inertial manifolds for a class of nonautonomo...In this paper, the long time behavior of nonautonomous infinite dimensional dynamical systems is discussed. Under the spectral gap condition. It is proved that there exist inertial manifolds for a class of nonautonomous evolution equations.展开更多
Optical fibers are seen in the optical sensing and optical fiber communication. Simultaneous propagation of optical pulses in an inhomogeneous optical fiber is described by a coupled time-dependent coefficient fourth-...Optical fibers are seen in the optical sensing and optical fiber communication. Simultaneous propagation of optical pulses in an inhomogeneous optical fiber is described by a coupled time-dependent coefficient fourth-order nonlinear Schr?dinger system, which is discussed in this paper. For such a system, we work out the Lax pair, Darboux transformation, and corresponding vector semi-rational nonautonomous rogue wave solutions. When the group velocity dispersion(GVD) and fourth-order dispersion(FOD) coefficients are the constants, we exhibit the first-and second-order vector semirational rogue waves which are composed of the four-petalled rogue waves and eye-shaped breathers. Both the width of the rogue wave along the time axis and temporal separation between the adjacent peaks of the breather decrease with the GVD coefficient or FOD coefficient. With the GVD and FOD coefficients as the linear, cosine, and exponential functions, we respectively present the first-and second-order periodic vector semi-rational rogue waves, first-and second-order asymmetry vector semi-rational rogue waves, and interactions between the eye-shaped breathers and the composite rogue waves.展开更多
A class of analytical solitary-wave solutions to the generalized nonautonomous cubic-quintic nonlinear Schrdinger equation with time- and space-modulated coefficients and potentials are constructed using the similar...A class of analytical solitary-wave solutions to the generalized nonautonomous cubic-quintic nonlinear Schrdinger equation with time- and space-modulated coefficients and potentials are constructed using the similarity transformation technique. Constraints for the dispersion coefficient, the cubic and quintic nonlinearities, the external potential, and the gain (loss) coefficient are presented at the same time. Various shapes of analytical solitary-wave solutions which have important applications of physical interest are studied in detail, such as the solutions in Feshbach resonance management with harmonic potentials, Faraday-type waves in the optical lattice potentials, and localized solutions supported by the Gaussian-shaped nonlinearity. The stability analysis of the solutions is discussed numerically.展开更多
In this paper, a nonautonomous eco-epidemiological model with disease in the predator is formulated and analyzed, in which saturated predation rate is taken into consideration. Under quite weak assumptions, sufficient...In this paper, a nonautonomous eco-epidemiological model with disease in the predator is formulated and analyzed, in which saturated predation rate is taken into consideration. Under quite weak assumptions, sufficient conditions for the permanence and extinction of the disease are obtained. Moreover, by constructing a Liapunov function, the global attractivity of the model is discussed. Finally, numerical simulations verified these results.展开更多
A nonautonomous schistosomiasis model with latent period and saturated incidence is investigated. Further, we study the long-time behavior of the epidemic model. The weaker sufficient conditions for the permanence and...A nonautonomous schistosomiasis model with latent period and saturated incidence is investigated. Further, we study the long-time behavior of the epidemic model. The weaker sufficient conditions for the permanence and extinction of infectious population of the model are obtained by constructing some auxiliary functions. Numerical simulations show agreement with the theoretical results.展开更多
In this paper, for controlling the spread of plant diseases, a nonautonomous SEIS (Susceptible → Exposed → Infectious → Susceptible) epidemic model with a general nonlinear incidence rate and time-varying impulsive...In this paper, for controlling the spread of plant diseases, a nonautonomous SEIS (Susceptible → Exposed → Infectious → Susceptible) epidemic model with a general nonlinear incidence rate and time-varying impulsive control strategy is proposed and investigated. This novel model could result in an objective criterion on how to control plant disease transmission by replanting of healthy plants and removal of infected plants. Using the method of small amplitude perturbation, the sufficient conditions under which guarantee the globally attractive of the disease-free periodic solution and the permanence of the disease are obtained, that is, the disease dies out if R12>1.展开更多
New theorems of asymptotical stability and uniformly asymptotical stability for nonautonomous difference equations are given in this paper. The classical Liapunov asymptotical stability theorem of nonautonomous differ...New theorems of asymptotical stability and uniformly asymptotical stability for nonautonomous difference equations are given in this paper. The classical Liapunov asymptotical stability theorem of nonautonomous difference equations relies on the existence of a positive definite Liapunov function that has an indefinitely small upper bound and whose variation along a given nonautonomous difference equations is negative definite. In this paper, we consider the case that the Liapunov function is only positive definite and its variation is semi-negative definite. At these weaker conditions, we put forward a new asymptotical stability theorem of nonautonomous difference equations by adding to extra conditions on the variation. After that, in addition to the hypotheses of our new asymptotical stability theorem, we obtain a new uniformly asymptotical stability theorem of nonautonomous difference equations provided that the Liapunov function has an indefinitely small upper bound. Example is given to verify our results in the last.展开更多
With the aid of a direct projective approach, a general transformation solution for the nonautonomous nonlinear Schr?dinger (NLS) system is derived. Based on certain known exact solutions of the projective equation, s...With the aid of a direct projective approach, a general transformation solution for the nonautonomous nonlinear Schr?dinger (NLS) system is derived. Based on certain known exact solutions of the projective equation, some periodic and localized excitations with novel properties are correspondingly revealed by entrancing appropriate system parameters. The integrable constraint conditions for the nonautonomous NLS system derived naturally here are consistent with the compatibility condition via the Painlevé analysis in other literature.展开更多
In this paper, the qualitative properties of general nonautonomous Lotka-Volterran-species competitive systems with impulsive e?ects are studied. Some new criteria on thepermanence, extinction and global attractivity ...In this paper, the qualitative properties of general nonautonomous Lotka-Volterran-species competitive systems with impulsive e?ects are studied. Some new criteria on thepermanence, extinction and global attractivity of partial species are established by used themethods of inequalities estimate and Liapunov functions. As applications, nonautonomous twospecies Lotka-Volterra systems with impulses are discussed.展开更多
This work is devoted to the study of the dynamics of one-dimensional monotone nonautonomous(cocycle) dynamical systems. A description of the structures of their invariant sets, omega limit sets,Bohr/Levitan almost per...This work is devoted to the study of the dynamics of one-dimensional monotone nonautonomous(cocycle) dynamical systems. A description of the structures of their invariant sets, omega limit sets,Bohr/Levitan almost periodic and almost automorphic motions, global attractors, and pinched and minimalsets is given. An application of our general results is given to scalar differential and difference equations.展开更多
In this paper, we consider the global existence of one-dimensional nonautonomous (inhomogeneous) Schrodinger flow. By exploiting geometric symmetries, we prove that, given a smooth initial map, the Cauchy problem of t...In this paper, we consider the global existence of one-dimensional nonautonomous (inhomogeneous) Schrodinger flow. By exploiting geometric symmetries, we prove that, given a smooth initial map, the Cauchy problem of the nonautonomous (inhomogeneous) Schrodinger flow from S1 into a Hermitian locally symmetric space admits a unique global smooth solution, and then we address the global existence of the Cauchy problem of inhomogeneous Heisenberg spin ferromagnet system.展开更多
This paper considers a class of discontinuous Galerkin method,which is constructed by Wong-Zakai approximation with the orthonormal Fourier basis,for numerically solving nonautonomous Stratonovich stochastic delay dif...This paper considers a class of discontinuous Galerkin method,which is constructed by Wong-Zakai approximation with the orthonormal Fourier basis,for numerically solving nonautonomous Stratonovich stochastic delay differential equations.We prove that the discontinuous Galerkin scheme is strongly convergent:globally stable and analogously asymptotically stable in mean square sense.In addition,this method can be easily extended to solve nonautonomous Stratonovich stochastic pantograph differential equations.Numerical tests indicate that the method has first-order and half-order strong mean square convergence,when the diffusion term is without delay and with delay,respectively.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos.11975172 and 12261131495)。
文摘To study controlled evolution of nonautonomous matter-wave breathers and rogue waves in spinor Bose–Einstein condensates with spatiotemporal modulation,we focus on a system of three coupled Gross–Pitaevskii equations with spacetime-dependent external potentials and temporally modulated gain-loss distributions.With different external potentials and gain-loss distributions,various solutions for controlled nonautonomous matterwave breathers and rogue waves are derived by the Darboux transformation method,such as breathers and rogue waves on arched and constant backgrounds which have the periodic and parabolic trajectories.Effects of the gain-loss distribution and linear potential on the breathers and rogue waves are studied.Nonautonomous two-breathers on the arched and constant backgrounds are also derived.
基金the National Natural Science Foundation of China (11871188, 12031019)。
文摘Let(X,φ) be a nonautonomous dynamical system.In this paper,we introduce the notions of packing topological entropy and measure-theoretical upper entropy for nonautonomous dynamical systems.Moreover,we establish the variational principle between the packing topological entropy and the measure-theoretical upper entropy.
文摘In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive release and general nonlinear incidence rate and investigate dynamical behaviors of the model. Under the reasonable assumptions, the sufficient conditions which guarantee the globally attractive of the disease-free periodic solution and the permanence of the infected fish are established, that is, the infected fish dies out if , whereas the disease persists if . To substantiate our theoretical results, extensive numerical simulations are performed for a hypothetical set of parameter values.
文摘In this paper the stability of nonlinear nonautonomous systems under the frequently-acting perturbation is studied.This study is a forward development of the study of thestability in the Liapunov sense;furthermore,it is of significance in practice sinceperturbations are often not single in the time domain.Malk in proved a general theoremabout thesubject.To apply the theorem,however,the user has to construct a Liapunovfunction which satisfies specified conditions and it is difficult to find such a function fornonlinear nonautonomous systems.In the light of the principle of Liapunov’s indirectmethod,which is an effective method to decide the stability of nonlinear systems in theLiapunov sense,the authors have achieved several important conclusions expressed in theform of theorems to determine the stability of nonlinear nonautonomous systems under thefrequently-acting perturbation.
文摘The long_time behaviour of a two_dimensional nonautonomous nonlinear Schrdinger equation is considered. The existence of uniform attractor is proved and the upper bound of the uniform attractor’s Hausdorff dimension is given.
文摘The necessary and sufficient condition of the stability of linear nonautonomous system under the frequently-acting perturbation has been given and proved on the basis of[1]and[2],and the theorem of the equivalence on the uniform and asymptotical stability in the sense of Liapunov and the stability under the frequently-acting perturbation of linear nonautonomous system has been given in this paper.Besides,the analysis of the dynamic stability of robot has been presented by applying the theorem in this paper,which is closer to reality.
文摘In this paper, the long time behavior of nonautonomous infinite dimensional dynamical systems is studied, A family of convergent approximate inertial manifolds for a class of evolution equations has been constructed when the spectral gap condition is satisfied.
文摘In this paper, the long time behavior of nonautonomous infinite dimensional dynamical systems is discussed. Under the spectral gap condition. It is proved that there exist inertial manifolds for a class of nonautonomous evolution equations.
基金Project supported by the BUPT Excellent Ph.D.Students Foundation(Grant No.CX2019201)the National Natural Science Foundation of China(Grant Nos.11772017 and 11805020)+1 种基金the Fund of State Key Laboratory of Information Photonics and Optical Communications(Beijing University of Posts and Telecommunications),China(Grant No.IPOC:2017ZZ05)the Fundamental Research Funds for the Central Universities of China(Grant No.2011BUPTYB02)。
文摘Optical fibers are seen in the optical sensing and optical fiber communication. Simultaneous propagation of optical pulses in an inhomogeneous optical fiber is described by a coupled time-dependent coefficient fourth-order nonlinear Schr?dinger system, which is discussed in this paper. For such a system, we work out the Lax pair, Darboux transformation, and corresponding vector semi-rational nonautonomous rogue wave solutions. When the group velocity dispersion(GVD) and fourth-order dispersion(FOD) coefficients are the constants, we exhibit the first-and second-order vector semirational rogue waves which are composed of the four-petalled rogue waves and eye-shaped breathers. Both the width of the rogue wave along the time axis and temporal separation between the adjacent peaks of the breather decrease with the GVD coefficient or FOD coefficient. With the GVD and FOD coefficients as the linear, cosine, and exponential functions, we respectively present the first-and second-order periodic vector semi-rational rogue waves, first-and second-order asymmetry vector semi-rational rogue waves, and interactions between the eye-shaped breathers and the composite rogue waves.
基金Project supported by the National Natural Science Foundation of China(Grant No.11175158)the Natural Science Foundation of Zhejiang Province of China(Grant No.LY12A04001)
文摘A class of analytical solitary-wave solutions to the generalized nonautonomous cubic-quintic nonlinear Schrdinger equation with time- and space-modulated coefficients and potentials are constructed using the similarity transformation technique. Constraints for the dispersion coefficient, the cubic and quintic nonlinearities, the external potential, and the gain (loss) coefficient are presented at the same time. Various shapes of analytical solitary-wave solutions which have important applications of physical interest are studied in detail, such as the solutions in Feshbach resonance management with harmonic potentials, Faraday-type waves in the optical lattice potentials, and localized solutions supported by the Gaussian-shaped nonlinearity. The stability analysis of the solutions is discussed numerically.
文摘In this paper, a nonautonomous eco-epidemiological model with disease in the predator is formulated and analyzed, in which saturated predation rate is taken into consideration. Under quite weak assumptions, sufficient conditions for the permanence and extinction of the disease are obtained. Moreover, by constructing a Liapunov function, the global attractivity of the model is discussed. Finally, numerical simulations verified these results.
文摘A nonautonomous schistosomiasis model with latent period and saturated incidence is investigated. Further, we study the long-time behavior of the epidemic model. The weaker sufficient conditions for the permanence and extinction of infectious population of the model are obtained by constructing some auxiliary functions. Numerical simulations show agreement with the theoretical results.
文摘In this paper, for controlling the spread of plant diseases, a nonautonomous SEIS (Susceptible → Exposed → Infectious → Susceptible) epidemic model with a general nonlinear incidence rate and time-varying impulsive control strategy is proposed and investigated. This novel model could result in an objective criterion on how to control plant disease transmission by replanting of healthy plants and removal of infected plants. Using the method of small amplitude perturbation, the sufficient conditions under which guarantee the globally attractive of the disease-free periodic solution and the permanence of the disease are obtained, that is, the disease dies out if R12>1.
文摘New theorems of asymptotical stability and uniformly asymptotical stability for nonautonomous difference equations are given in this paper. The classical Liapunov asymptotical stability theorem of nonautonomous difference equations relies on the existence of a positive definite Liapunov function that has an indefinitely small upper bound and whose variation along a given nonautonomous difference equations is negative definite. In this paper, we consider the case that the Liapunov function is only positive definite and its variation is semi-negative definite. At these weaker conditions, we put forward a new asymptotical stability theorem of nonautonomous difference equations by adding to extra conditions on the variation. After that, in addition to the hypotheses of our new asymptotical stability theorem, we obtain a new uniformly asymptotical stability theorem of nonautonomous difference equations provided that the Liapunov function has an indefinitely small upper bound. Example is given to verify our results in the last.
文摘With the aid of a direct projective approach, a general transformation solution for the nonautonomous nonlinear Schr?dinger (NLS) system is derived. Based on certain known exact solutions of the projective equation, some periodic and localized excitations with novel properties are correspondingly revealed by entrancing appropriate system parameters. The integrable constraint conditions for the nonautonomous NLS system derived naturally here are consistent with the compatibility condition via the Painlevé analysis in other literature.
基金Supported by The National Natural Science Foundation of P.R. China [60764003]The Scientific Research Programmes of Colleges in Xinjiang [XJEDU2007G01, XJEDU2006I05]+1 种基金The National Key Technologies R & D Program of China [2008BAI68B01]The Natural Science Foundation of Jiangxi Province [2008GZS0027]
文摘In this paper, the qualitative properties of general nonautonomous Lotka-Volterran-species competitive systems with impulsive e?ects are studied. Some new criteria on thepermanence, extinction and global attractivity of partial species are established by used themethods of inequalities estimate and Liapunov functions. As applications, nonautonomous twospecies Lotka-Volterra systems with impulses are discussed.
基金supported by the State Program of the Republic of Moldova “Multivalued Dynamical Systems, Singular Perturbations, Integral Operators and Non-Associative Algebraic Structures (Grant No. 20.80009.5007.25)”
文摘This work is devoted to the study of the dynamics of one-dimensional monotone nonautonomous(cocycle) dynamical systems. A description of the structures of their invariant sets, omega limit sets,Bohr/Levitan almost periodic and almost automorphic motions, global attractors, and pinched and minimalsets is given. An application of our general results is given to scalar differential and difference equations.
基金We would like to thank Kung-Ching Chang and Wei-Yue Ding for their valuablecomments and helpful discussions. This work was partially supported by National University of Singapore Academic Research Fund (Grant RP3982718) the National Natural Science F
文摘In this paper, we consider the global existence of one-dimensional nonautonomous (inhomogeneous) Schrodinger flow. By exploiting geometric symmetries, we prove that, given a smooth initial map, the Cauchy problem of the nonautonomous (inhomogeneous) Schrodinger flow from S1 into a Hermitian locally symmetric space admits a unique global smooth solution, and then we address the global existence of the Cauchy problem of inhomogeneous Heisenberg spin ferromagnet system.
基金the National Natural Science Foundation of China(No.11671343).
文摘This paper considers a class of discontinuous Galerkin method,which is constructed by Wong-Zakai approximation with the orthonormal Fourier basis,for numerically solving nonautonomous Stratonovich stochastic delay differential equations.We prove that the discontinuous Galerkin scheme is strongly convergent:globally stable and analogously asymptotically stable in mean square sense.In addition,this method can be easily extended to solve nonautonomous Stratonovich stochastic pantograph differential equations.Numerical tests indicate that the method has first-order and half-order strong mean square convergence,when the diffusion term is without delay and with delay,respectively.
