A complete approximate symmetry classification of a class of perturbed nonlinear wave equations isperformed using the method originated from Fushchich and Shtelen.Moreover,large classes of approximate invariantsolutio...A complete approximate symmetry classification of a class of perturbed nonlinear wave equations isperformed using the method originated from Fushchich and Shtelen.Moreover,large classes of approximate invariantsolutions of the equations based on the Lie group method are constructed.展开更多
In this paper,a new nonlinear autonomous system introduced by Chlouverakis and Sprott is studied further,to present very rich and complex nonlinear dynamical behaviors. Some basic dynamical properties are studied eith...In this paper,a new nonlinear autonomous system introduced by Chlouverakis and Sprott is studied further,to present very rich and complex nonlinear dynamical behaviors. Some basic dynamical properties are studied either analytically or nu-merically,such as Poincaré map,Lyapunov exponents and Lyapunov dimension. Based on this flow,a new almost-Hamilton chaotic system with very high Lyapunov dimensions is constructed and investigated. Two new nonlinear autonomous systems can be changed into one another by adding or omitting some constant coefficients.展开更多
In this paper the Lie symmetry and conserved quantities for nonholonomic Vacco dynamical systems are studied. The determining equation of the Lie symmetry for the system is given. The general Hojman conserved quantity...In this paper the Lie symmetry and conserved quantities for nonholonomic Vacco dynamical systems are studied. The determining equation of the Lie symmetry for the system is given. The general Hojman conserved quantity and the Lutzky conserved quantity deduced from the symmetry are obtained.展开更多
The explicit expressions for indecomposable representations of nine square-root Lie algebras of vector type, , are obtained on the space of universal enveloping algebra of two-state Heisenberg–Weyl algebra, the invar...The explicit expressions for indecomposable representations of nine square-root Lie algebras of vector type, , are obtained on the space of universal enveloping algebra of two-state Heisenberg–Weyl algebra, the invariant subspaces and the quotient spaces. From Fock representations corresponding to these indecomposable representations, the inhomogeneous boson realizations of are given. The expectation values of in the angular momentum coherent states are calculated as well as the corresponding classical limits.展开更多
Parametric resonance can lead to dangerously large rolling motions, endangering the ship, cargo and crew. The QR-faetorization method for calculating (LCEs) Lyapunov Characteristic Exponents was introduced; parametr...Parametric resonance can lead to dangerously large rolling motions, endangering the ship, cargo and crew. The QR-faetorization method for calculating (LCEs) Lyapunov Characteristic Exponents was introduced; parametric resonance stability of ships in longitudinal waves was then analyzed using LCEs. Then the safe and unsafe regions of target ships were then identified. The results showed that this method can be used to analyze ship stability and to accurately identify safe and unsafe operating conditions for a ship in longitudinal waves.展开更多
The dynamical Lie algebraic method is used for the description of statistical mechanics of rotationally inelastic molecule-surface scattering. It can give the time-evolution operators about the low power of and by s...The dynamical Lie algebraic method is used for the description of statistical mechanics of rotationally inelastic molecule-surface scattering. It can give the time-evolution operators about the low power of and by solving a set of coupled nonlinear differential equations. For considering the contribution of the high power of and , we use the Magnus formula. Thus, with the time-evolution operators we can get the statistical average values of the measurable quantities in terms of the density operator formalism in statistical mechanics. The method is applied to the scattering of (rigid rotor) by a flat, rigid surface to illustrate its general procedure. The results demonstrate that the method is useful for describing the statistical dynamics of gas-surface scattering.展开更多
Some rodent-dispersed seeds have a hard seed-coat(e.g.woody endocarp).Specific scrapes or dental marks on the hard seed-coat left by rodents when they eat these seeds can be used to identify seed predators.In this stu...Some rodent-dispersed seeds have a hard seed-coat(e.g.woody endocarp).Specific scrapes or dental marks on the hard seed-coat left by rodents when they eat these seeds can be used to identify seed predators.In this study we measured the morphological traits of endocarp-remains of seeds of wild apricot Prunus armeniaca used by Chinese white-bellied rats Niviventor confucianus and Korean field mice Apodemus peninsulae.We established their Fisher's linear discriminant functions to separate endocarp-remains between the two predators.A total of 90.0% of the endocarp-remains left by Korean field mice and 88.0% of those left by Chinese white-bellied rats were correctly classified.The overall percentage of correct classification was 89.0%.One hundred and sixty endocarp-remains of unknown what species predated them were classified using the functions.The method may allow more reliable quantitative studies of the effects of Chinese white-bellied rats and Korean field mice on seed consumption and dispersal of wild apricot and this study might be used for reference in other studies of seed predators identification on hard seeds.展开更多
In this paper, the Noether Lie symmetry and conserved quantities of generalized classical mechanical system are studied. The definition and the criterion of the Noether Lie symmetry for the system under the general in...In this paper, the Noether Lie symmetry and conserved quantities of generalized classical mechanical system are studied. The definition and the criterion of the Noether Lie symmetry for the system under the general infinitesimal transformations of groups are given. The Noether conserved quantity and the Hojman conserved quantity deduced from the Noether Lie symmetry are obtained. An example is given to illustrate the application of the results.展开更多
In this paper, with parametric uncertainties such as the mass of vehicle, the inertia of vehicle about vertical axis, and the tire cornering stiffness, we deal with the vehicle lateral control problem in intelligent v...In this paper, with parametric uncertainties such as the mass of vehicle, the inertia of vehicle about vertical axis, and the tire cornering stiffness, we deal with the vehicle lateral control problem in intelligent vehicle systems. Based on the dynamical model of vehicle, by applying Lyapunov function method, the control problem for lane keeping in the presence of parametric uncertainty is studied, the direct adaptive algorithm to compensate for parametric variations is proposed and the terminal sliding mode variable structure control laws are designed with look-ahead references systems. The stability of the system is investigated from the zero dynamics analysis. Simulation results show that convergence rates of the lateral displacement error, yaw angle error and slid angle are fast.展开更多
As an analytical method, the effective-field theory (EFT) is used to study the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field. The effective-field equations of motion...As an analytical method, the effective-field theory (EFT) is used to study the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field. The effective-field equations of motion of the average magnetization are given for the honeycomb lattice (Z = 3). The Liapunov exponent A is calculated for discussing the stability of the magnetization and it is used to determine the phase boundary. In the field amplitude ho / ZJ-temperature T/ZJ plane, the phase boundary separating the dynamic ordered and the disordered phase has been drawn. In contrast to previous analytical results that predicted a tricritical point separating a dynamic phase boundary line of continuous and discontinuous transitions, we find that the transition is always continuous. There is inconsistency between our results and previous analytical results, because they do not introduce sufficiently strong fluctuations.展开更多
This paper studies the global exponential synchronization of uncertain complex delayed dynamical networks. The network model considered is general dynamical delay networks with unknown network structure and unknown co...This paper studies the global exponential synchronization of uncertain complex delayed dynamical networks. The network model considered is general dynamical delay networks with unknown network structure and unknown coupling functions but bounded. Novel delay-dependent linear controllers are designed via the Lyapunov stability theory. Especially, it is shown that the controlled networks are globally exponentially synchronized with a given convergence rate. An example of typical dynamical network of this class, having the Lorenz system at each node, has been used to demonstrate and verify the novel design proposed. And, the numerical simulation results show the effectiveness of proposed synchronization approaches.展开更多
The presence of Geotrichum candidum in fresh cheese is considered to be a contaminant and may lead to the product spoilage. The oxidative yeast Candida maltosa firstly isolated from the spoiled fruit yoghurt surface i...The presence of Geotrichum candidum in fresh cheese is considered to be a contaminant and may lead to the product spoilage. The oxidative yeast Candida maltosa firstly isolated from the spoiled fruit yoghurt surface in Slovakia belongs to the yeast contaminants of fermented dairy products. The effect of the cultivation temperature and the presence of Lactobacillus rhamnosus GG on the growth of dairy spoilage yeasts in ultrapasteurized milk was studied. Addition of Lb. rhamnosus GG in milk caused partial inhibition of the yeast growth dynamics in milk. The water activity transformation of Gibson model after the temperature modification (Tw) was applied to model growth dynamics of G. candidum in pure and mixed culture, respectively: In μ_Gc=-5.0376+2.7281 Tw-0.4217Tw^2, lnμ_CC_LGG=-6.0033+3.2996Tw-0.5553Tw^2. The effect of different Lb. rhamnosus GG addition and the incubation temperature on the C. maltosa growth dynamics was analyzed by linear regression methodology and described by using following equations: lnGr1=-5.3674+0.2341T+0.2599N0-0.0032T^2-0.0492N0^2-0.0068TN0 and lnGr11=-9.5457-0.249T+2.3823N0 +0.0099T^2-0.2324N0^2+0.0098TN0 Based on the principles of predictive microbiology, the mutual microbial interactions and potential application of the lactobacillus strains in food protection are discussed.展开更多
Some sufficient conditions for oscillation of the generalized Lienard equations x = h(y) - F(x), y=-g(x) are given, which generalize the results of [1-7].
In this paper, we derive a time-delayed and diffusive echinococcosis transmission model. We first address the well-posedness to the initial-value problem for the model and give the basic reproduction number TO0. In th...In this paper, we derive a time-delayed and diffusive echinococcosis transmission model. We first address the well-posedness to the initial-value problem for the model and give the basic reproduction number TO0. In the case of a bounded spatial domain, we establish the local stability as well as the global stability of the disease-free and disease equilibria of the model. The methods to prove the local and the global stability are to analyze the corresponding characteristic equations and construct Lyapunov functionals, respectively. In the case of an unbounded spatial domain, by applying Schauder's fixed point theorem and the limiting arguments, we show that when R0 〉 1, there exists a constant c* 〉 0 such that the model admits positive traveling wave solutions connecting the disease-free and endemic equilibrium for c 〉 c*, and when R0 〉 1 and c 〈 c*, the model has no positive traveling wave solutions connecting them.展开更多
In this paper, a diffusive hepatitis B virus (HBV) infection model with a discrete time delay is presented and analyzed, where the spatial mobility of both intracellular capsid covered HBV DNA and HBV and the intrac...In this paper, a diffusive hepatitis B virus (HBV) infection model with a discrete time delay is presented and analyzed, where the spatial mobility of both intracellular capsid covered HBV DNA and HBV and the intracellular delay in the reproduction of infected hepatocytes are taken into account. We define the basic reproduction number R0 that determines the dynamical behavior of the model. The local and global stability of the spatially homogeneous steady states are analyzed by using the linearization technique and the direct Lyapunov method, respectively. It is shown that the susceptible uninfected steady state is globally asymptotically stable whenever R0 ≤i and is unstable whenever R0 〉1. Also, the infected steady state is globally asymptotically stable when R0 〉 1. Finally, numerical simulations are carried out to illustrate the results obtained.展开更多
文摘A complete approximate symmetry classification of a class of perturbed nonlinear wave equations isperformed using the method originated from Fushchich and Shtelen.Moreover,large classes of approximate invariantsolutions of the equations based on the Lie group method are constructed.
基金Project supported by the National Natural Science Foundation of China (No. 50475109)the Natural Science Foundation of Gansu Province (No. 3ZS-042-B25-049), China
文摘In this paper,a new nonlinear autonomous system introduced by Chlouverakis and Sprott is studied further,to present very rich and complex nonlinear dynamical behaviors. Some basic dynamical properties are studied either analytically or nu-merically,such as Poincaré map,Lyapunov exponents and Lyapunov dimension. Based on this flow,a new almost-Hamilton chaotic system with very high Lyapunov dimensions is constructed and investigated. Two new nonlinear autonomous systems can be changed into one another by adding or omitting some constant coefficients.
文摘In this paper the Lie symmetry and conserved quantities for nonholonomic Vacco dynamical systems are studied. The determining equation of the Lie symmetry for the system is given. The general Hojman conserved quantity and the Lutzky conserved quantity deduced from the symmetry are obtained.
文摘The explicit expressions for indecomposable representations of nine square-root Lie algebras of vector type, , are obtained on the space of universal enveloping algebra of two-state Heisenberg–Weyl algebra, the invariant subspaces and the quotient spaces. From Fock representations corresponding to these indecomposable representations, the inhomogeneous boson realizations of are given. The expectation values of in the angular momentum coherent states are calculated as well as the corresponding classical limits.
文摘Parametric resonance can lead to dangerously large rolling motions, endangering the ship, cargo and crew. The QR-faetorization method for calculating (LCEs) Lyapunov Characteristic Exponents was introduced; parametric resonance stability of ships in longitudinal waves was then analyzed using LCEs. Then the safe and unsafe regions of target ships were then identified. The results showed that this method can be used to analyze ship stability and to accurately identify safe and unsafe operating conditions for a ship in longitudinal waves.
基金The project supported by Natural Science Foundation of Shandong Province of China+2 种基金National Natural Science Foundation of Chinathe Doctor Foundation of the Ministry of Education of China
文摘The dynamical Lie algebraic method is used for the description of statistical mechanics of rotationally inelastic molecule-surface scattering. It can give the time-evolution operators about the low power of and by solving a set of coupled nonlinear differential equations. For considering the contribution of the high power of and , we use the Magnus formula. Thus, with the time-evolution operators we can get the statistical average values of the measurable quantities in terms of the density operator formalism in statistical mechanics. The method is applied to the scattering of (rigid rotor) by a flat, rigid surface to illustrate its general procedure. The results demonstrate that the method is useful for describing the statistical dynamics of gas-surface scattering.
基金funded by the National Natural Science Foundation of China(30800120) and the Foundation for New Teachers of Huazhong Normal University
文摘Some rodent-dispersed seeds have a hard seed-coat(e.g.woody endocarp).Specific scrapes or dental marks on the hard seed-coat left by rodents when they eat these seeds can be used to identify seed predators.In this study we measured the morphological traits of endocarp-remains of seeds of wild apricot Prunus armeniaca used by Chinese white-bellied rats Niviventor confucianus and Korean field mice Apodemus peninsulae.We established their Fisher's linear discriminant functions to separate endocarp-remains between the two predators.A total of 90.0% of the endocarp-remains left by Korean field mice and 88.0% of those left by Chinese white-bellied rats were correctly classified.The overall percentage of correct classification was 89.0%.One hundred and sixty endocarp-remains of unknown what species predated them were classified using the functions.The method may allow more reliable quantitative studies of the effects of Chinese white-bellied rats and Korean field mice on seed consumption and dispersal of wild apricot and this study might be used for reference in other studies of seed predators identification on hard seeds.
文摘In this paper, the Noether Lie symmetry and conserved quantities of generalized classical mechanical system are studied. The definition and the criterion of the Noether Lie symmetry for the system under the general infinitesimal transformations of groups are given. The Noether conserved quantity and the Hojman conserved quantity deduced from the Noether Lie symmetry are obtained. An example is given to illustrate the application of the results.
基金Sponsored by the National Natural Science Foundation of China(Grant No.10772152)
文摘In this paper, with parametric uncertainties such as the mass of vehicle, the inertia of vehicle about vertical axis, and the tire cornering stiffness, we deal with the vehicle lateral control problem in intelligent vehicle systems. Based on the dynamical model of vehicle, by applying Lyapunov function method, the control problem for lane keeping in the presence of parametric uncertainty is studied, the direct adaptive algorithm to compensate for parametric variations is proposed and the terminal sliding mode variable structure control laws are designed with look-ahead references systems. The stability of the system is investigated from the zero dynamics analysis. Simulation results show that convergence rates of the lateral displacement error, yaw angle error and slid angle are fast.
文摘As an analytical method, the effective-field theory (EFT) is used to study the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field. The effective-field equations of motion of the average magnetization are given for the honeycomb lattice (Z = 3). The Liapunov exponent A is calculated for discussing the stability of the magnetization and it is used to determine the phase boundary. In the field amplitude ho / ZJ-temperature T/ZJ plane, the phase boundary separating the dynamic ordered and the disordered phase has been drawn. In contrast to previous analytical results that predicted a tricritical point separating a dynamic phase boundary line of continuous and discontinuous transitions, we find that the transition is always continuous. There is inconsistency between our results and previous analytical results, because they do not introduce sufficiently strong fluctuations.
文摘This paper studies the global exponential synchronization of uncertain complex delayed dynamical networks. The network model considered is general dynamical delay networks with unknown network structure and unknown coupling functions but bounded. Novel delay-dependent linear controllers are designed via the Lyapunov stability theory. Especially, it is shown that the controlled networks are globally exponentially synchronized with a given convergence rate. An example of typical dynamical network of this class, having the Lorenz system at each node, has been used to demonstrate and verify the novel design proposed. And, the numerical simulation results show the effectiveness of proposed synchronization approaches.
文摘The presence of Geotrichum candidum in fresh cheese is considered to be a contaminant and may lead to the product spoilage. The oxidative yeast Candida maltosa firstly isolated from the spoiled fruit yoghurt surface in Slovakia belongs to the yeast contaminants of fermented dairy products. The effect of the cultivation temperature and the presence of Lactobacillus rhamnosus GG on the growth of dairy spoilage yeasts in ultrapasteurized milk was studied. Addition of Lb. rhamnosus GG in milk caused partial inhibition of the yeast growth dynamics in milk. The water activity transformation of Gibson model after the temperature modification (Tw) was applied to model growth dynamics of G. candidum in pure and mixed culture, respectively: In μ_Gc=-5.0376+2.7281 Tw-0.4217Tw^2, lnμ_CC_LGG=-6.0033+3.2996Tw-0.5553Tw^2. The effect of different Lb. rhamnosus GG addition and the incubation temperature on the C. maltosa growth dynamics was analyzed by linear regression methodology and described by using following equations: lnGr1=-5.3674+0.2341T+0.2599N0-0.0032T^2-0.0492N0^2-0.0068TN0 and lnGr11=-9.5457-0.249T+2.3823N0 +0.0099T^2-0.2324N0^2+0.0098TN0 Based on the principles of predictive microbiology, the mutual microbial interactions and potential application of the lactobacillus strains in food protection are discussed.
文摘Some sufficient conditions for oscillation of the generalized Lienard equations x = h(y) - F(x), y=-g(x) are given, which generalize the results of [1-7].
文摘In this paper, we derive a time-delayed and diffusive echinococcosis transmission model. We first address the well-posedness to the initial-value problem for the model and give the basic reproduction number TO0. In the case of a bounded spatial domain, we establish the local stability as well as the global stability of the disease-free and disease equilibria of the model. The methods to prove the local and the global stability are to analyze the corresponding characteristic equations and construct Lyapunov functionals, respectively. In the case of an unbounded spatial domain, by applying Schauder's fixed point theorem and the limiting arguments, we show that when R0 〉 1, there exists a constant c* 〉 0 such that the model admits positive traveling wave solutions connecting the disease-free and endemic equilibrium for c 〉 c*, and when R0 〉 1 and c 〈 c*, the model has no positive traveling wave solutions connecting them.
文摘In this paper, a diffusive hepatitis B virus (HBV) infection model with a discrete time delay is presented and analyzed, where the spatial mobility of both intracellular capsid covered HBV DNA and HBV and the intracellular delay in the reproduction of infected hepatocytes are taken into account. We define the basic reproduction number R0 that determines the dynamical behavior of the model. The local and global stability of the spatially homogeneous steady states are analyzed by using the linearization technique and the direct Lyapunov method, respectively. It is shown that the susceptible uninfected steady state is globally asymptotically stable whenever R0 ≤i and is unstable whenever R0 〉1. Also, the infected steady state is globally asymptotically stable when R0 〉 1. Finally, numerical simulations are carried out to illustrate the results obtained.