In this paper, the problem of determining the largest possible set of symmetries for an important nonlinear dynamical system： the two-dimensional damped Kuramoto-Sivashinsky （（21）） DKS ） equation is studied. By ...In this paper, the problem of determining the largest possible set of symmetries for an important nonlinear dynamical system： the two-dimensional damped Kuramoto-Sivashinsky （（21）） DKS ） equation is studied. By applying the basic Lie symmetry method for the （217）） DKS equation, the classical Lie point symmetry operators are obtained. Also, the optimal system of one-dimensional subalgebras of the equation is constructed. The Lie invariants as well as similarity reduced equations corresponding to infinitesimal symmetries are obtained. The nonclassicaJ symmetries of the （2D） DKS equation are also investigated.展开更多
Traditional biomechanical analyses of human movement are generally derived from linear mathematics.While these methods can be useful in many situations,they do not describe behaviors in human systems that are predomin...Traditional biomechanical analyses of human movement are generally derived from linear mathematics.While these methods can be useful in many situations,they do not describe behaviors in human systems that are predominately nonlinear.For this reason,nonlinear analysis methods based on a dynamical systems approach have become more prevalent in recent literature.These analysis techniques have provided new insights into how systems(1) maintain pattern stability,(2) transition into new states,and(3) are governed by short-and long-term(fractal) correlational processes at different spatio-temporal scales.These different aspects of system dynamics are typically investigated using concepts related to variability,stability,complexity,and adaptability.The purpose of this paper is to compare and contrast these different concepts and demonstrate that,although related,these terms represent fundamentally different aspects of system dynamics.In particular,we argue that variability should not uniformly be equated with stability or complexity of movement.In addition,current dynamic stability measures based on nonlinear analysis methods(such as the finite maximal Lyapunov exponent) can reveal local instabilities in movement dynamics,but the degree to which these local instabilities relate to global postural and gait stability and the ability to resist external perturbations remains to be explored.Finally,systematic studies are needed to relate observed reductions in complexity with aging and disease to the adaptive capabilities of the movement system and how complexity changes as a function of different task constraints.展开更多
Dynamic equations of motional flexible beam elements were derived considering second-order effect. Non-linear finite element method and three-node Euler-Bernoulli beam elements were used. Because accuracy is higher in...Dynamic equations of motional flexible beam elements were derived considering second-order effect. Non-linear finite element method and three-node Euler-Bernoulli beam elements were used. Because accuracy is higher in non-linear structural analysis,three-node beam elements are used to deduce shape functions and stiffness matrices in dynamic equations of flexible elements. Static condensation method was used to obtain the finial dynamic equations of three-node beam elements. According to geometrical relations of nodal displacements in concomitant and global coordinate system,dynamic equations of elements can be transformed to global coordinate system by concomitant coordinate method in order to build the global dynamic equations. Analyzed amplitude condition of flexible arm support of a port crane,the results show that second-order effect should be considered in kinetic-elastic analysis for heavy load machinery of big flexibility.展开更多
In this paper,by using bilinear form and extended homoclinic test approach,we obtain new breather-type periodic soliton solutions of the (1+1)-dimensional Sinh-Poisson equation.These results demonstrate that the nonli...In this paper,by using bilinear form and extended homoclinic test approach,we obtain new breather-type periodic soliton solutions of the (1+1)-dimensional Sinh-Poisson equation.These results demonstrate that the nonlinear evolution equation has rich dynamical behavior even if it is (1+1)-dimensional.展开更多
This paper presents a robust nonlinear controller design approach for uncertain quadrotors to implement trajectory tracking missions. The quaternion representation is applied to describe the rotational dynamics in ord...This paper presents a robust nonlinear controller design approach for uncertain quadrotors to implement trajectory tracking missions. The quaternion representation is applied to describe the rotational dynamics in order to avoid the singularity problem existing in the Euler angle representation. A nonlinear robust controller is proposed, which consists of an attitude controller to stabilize the rotational motions and a position controller to control translational motions. The quadrotor dynamics involves uncertainties such as parameter uncertainties, nonlinearities, and external disturbances and their effects on closed-loop control system can be guaranteed to be restrained. Simulation results on the quadrotor demonstrate the effectiveness of the designed control approach.展开更多
The recently developed short-time linear response algorithm,which predicts the response of a nonlinear chaotic forced-dissipative system to small external perturbation,yields high precision of the response prediction....The recently developed short-time linear response algorithm,which predicts the response of a nonlinear chaotic forced-dissipative system to small external perturbation,yields high precision of the response prediction.However,the computation of the short-time linear response formula with the full rank tangent map can be expensive.Here,a numerical method to potentially overcome the increasing numerical complexity for large scale models with many variables by using the reduced-rank tangent map in the computation is proposed.The conditions for which the short-time linear response approximation with the reduced-rank tangent map is valid are established,and two practical situations are examined,where the response to small external perturbations is predicted for nonlinear chaotic forced-dissipative systems with different dynamical properties.展开更多
In this paper,the rogue waves of the higher-order dispersive nonlinear Schrdinger(HDNLS) equation are investigated,which describes the propagation of ultrashort optical pulse in optical fibers.The rogue wave solutions...In this paper,the rogue waves of the higher-order dispersive nonlinear Schrdinger(HDNLS) equation are investigated,which describes the propagation of ultrashort optical pulse in optical fibers.The rogue wave solutions of HDNLS equation are constructed by using the modified Darboux transformation method.The explicit first and secondorder rogue wave solutions are presented under the plane wave seeding solution background.The nonlinear dynamics and properties of rogue waves are discussed by analyzing the obtained rational solutions.The influence of little perturbation on the rogue waves is discussed with the help of graphical simulation.展开更多
The paper addresses the system performance of coal-fired power unit with changed auxiliary system or other local heat disturbance. The idea of state space model is imported and the universal formula for the calculatio...The paper addresses the system performance of coal-fired power unit with changed auxiliary system or other local heat disturbance. The idea of state space model is imported and the universal formula for the calculation of system performance output is deduced on the system state equation. Two important vector of system are worked out under linear system assumption and transform. The transfer matrix is the characteristics of system itself and is constant for a similar condition, which greatly facilitates the analysis. The concept of thermal disturbance vector is proposed to construct the thermal disturbance input easily. The method can be helpful for analyzing any thermal disturbance input satisfying the assumption and also for supplementing the correction means of performance test. An example of 600MW power unit is presented to demonstrate its availability.展开更多
The dynamical behaviors of a two-species discrete ratio-dependent predator-prey sys- tem are considered. Some sufficient conditions for the local stability of the equilibria is obtained by using the linearization meth...The dynamical behaviors of a two-species discrete ratio-dependent predator-prey sys- tem are considered. Some sufficient conditions for the local stability of the equilibria is obtained by using the linearization method. Further, we also obtain a new sufficient condition to ensure that the positive equilibrium is globally asymptotically stable by using an iteration scheme and the comparison principle of difference equations, which generalizes what paper [G. Chen, Z. Teng and Z. Hu, Analysis of stability for a discrete ratio-dependent predator-prey system, Indian J. Pure Appl. Math. 42（1） （2011） 1-26] has done. The method given in this paper is new and very resultful comparing with papers [H. F. Huo and W. T. Li, Existence and global stability of periodic solutions of a discrete predator--prey system with delays, Appl. Math. Comput. 153 （2004） 337-351; X. Liao, S. Zhou and Y. Chen, On permanence and global stability in a general Gilpin- Ayala competition predator prey discrete system, Appl. Math. Comput. 190 （2007） 500-509] and it can also be applied to study the global asymptotic stability for general multiple species discrete population systems. At the end of this paper, we present an open question.展开更多
The paper presents the formulation to compute numerically the unsteady aerodynamic forces on the vibrating annular cascade blades.The formulation is based on the finite volume method.By applying the TVD scheme to the ...The paper presents the formulation to compute numerically the unsteady aerodynamic forces on the vibrating annular cascade blades.The formulation is based on the finite volume method.By applying the TVD scheme to the linear unsteady calculations,the precise calculation of the peak of unsteady aerodynamic forces at the shock wave location like the delta function singularity becomes possible without empirical constants.As a further feature of the present paper,results of the present numerical calculation are compared with those of the double linearization theory(DLT),which assumes small unsteady and steady disturbances but the unsteady disturbances are much smaller than the steady disturbances.Since DLT requires far less computational resources than the present numerical calculation,the validation of DLT is quite important from the engineering point of view.Under the conditions of small steady disturbances,a good agreement between these two results is observed,so that the two codes are cross-validated.The comparison also reveals the limitation on the applicability of DLT.展开更多
In this paper the liquid argon nanojet break-up phenomenon was studied using the molecular dynamics method. The effects of temperature, nozzle diameter and body force on the nanojet break-up length and time were simu-...In this paper the liquid argon nanojet break-up phenomenon was studied using the molecular dynamics method. The effects of temperature, nozzle diameter and body force on the nanojet break-up length and time were simu- lated. Meanwhile, the particle size, wave length and the frequency of the disturbance were compared with the re- suits of linear stability analysis. The results showed that even though the fluid becomes discontinuous, the tradi- tional linear stability analysis can be used to make a rough calculation of the nanojet break-up.展开更多
A general and efficient method is presented in this paper for studying the effects of unbalance on the breathing mechanism of crack.Based on 3D finite element models combined with a nonlinear contact approach for crac...A general and efficient method is presented in this paper for studying the effects of unbalance on the breathing mechanism of crack.Based on 3D finite element models combined with a nonlinear contact approach for crack modeling, the method is free from theassumption of weight-dominance and can be used to gain deep insights into the breathing mechanism of crack. In order to greatlyreduce the computational time, a complex free-interface component mode synthesis (CMS) method is employed to reduce theorder of the model. Based on the proposed method, the effects of unbalance on the breathing mechanism of crack are discussed.Numerical results show that the unbalance can lead to significant changes in the breathing of crack, even when the unbalance force is about an order of magnitude smaller than the self-weight. Moreover, the level and orientation of the unbalance have also remarkable effects on the breathing behaviors of crack. Besides, a new universal non-steady breathing phenomenon of crack is firstly found in this paper, which denotes that the breathing speed of a crack is fluctuated over one revolution when there exists residual unbalance in the cracked rotor.展开更多
文摘In this paper, the problem of determining the largest possible set of symmetries for an important nonlinear dynamical system： the two-dimensional damped Kuramoto-Sivashinsky （（21）） DKS ） equation is studied. By applying the basic Lie symmetry method for the （217）） DKS equation, the classical Lie point symmetry operators are obtained. Also, the optimal system of one-dimensional subalgebras of the equation is constructed. The Lie invariants as well as similarity reduced equations corresponding to infinitesimal symmetries are obtained. The nonclassicaJ symmetries of the （2D） DKS equation are also investigated.
文摘Traditional biomechanical analyses of human movement are generally derived from linear mathematics.While these methods can be useful in many situations,they do not describe behaviors in human systems that are predominately nonlinear.For this reason,nonlinear analysis methods based on a dynamical systems approach have become more prevalent in recent literature.These analysis techniques have provided new insights into how systems(1) maintain pattern stability,(2) transition into new states,and(3) are governed by short-and long-term(fractal) correlational processes at different spatio-temporal scales.These different aspects of system dynamics are typically investigated using concepts related to variability,stability,complexity,and adaptability.The purpose of this paper is to compare and contrast these different concepts and demonstrate that,although related,these terms represent fundamentally different aspects of system dynamics.In particular,we argue that variability should not uniformly be equated with stability or complexity of movement.In addition,current dynamic stability measures based on nonlinear analysis methods(such as the finite maximal Lyapunov exponent) can reveal local instabilities in movement dynamics,but the degree to which these local instabilities relate to global postural and gait stability and the ability to resist external perturbations remains to be explored.Finally,systematic studies are needed to relate observed reductions in complexity with aging and disease to the adaptive capabilities of the movement system and how complexity changes as a function of different task constraints.
文摘Dynamic equations of motional flexible beam elements were derived considering second-order effect. Non-linear finite element method and three-node Euler-Bernoulli beam elements were used. Because accuracy is higher in non-linear structural analysis,three-node beam elements are used to deduce shape functions and stiffness matrices in dynamic equations of flexible elements. Static condensation method was used to obtain the finial dynamic equations of three-node beam elements. According to geometrical relations of nodal displacements in concomitant and global coordinate system,dynamic equations of elements can be transformed to global coordinate system by concomitant coordinate method in order to build the global dynamic equations. Analyzed amplitude condition of flexible arm support of a port crane,the results show that second-order effect should be considered in kinetic-elastic analysis for heavy load machinery of big flexibility.
基金Supported by the Natural Science Foundation of China under Grant No. 10971169Sichuan Educational Science Foundation under Grant No. 09zc008
文摘In this paper,by using bilinear form and extended homoclinic test approach,we obtain new breather-type periodic soliton solutions of the (1+1)-dimensional Sinh-Poisson equation.These results demonstrate that the nonlinear evolution equation has rich dynamical behavior even if it is (1+1)-dimensional.
基金supported by National High-Tech R&D Program of China (863 Program) (Grant No. 2012AA112201)National Natural Science Foundation of China (Grant No. 61503012)
文摘This paper presents a robust nonlinear controller design approach for uncertain quadrotors to implement trajectory tracking missions. The quaternion representation is applied to describe the rotational dynamics in order to avoid the singularity problem existing in the Euler angle representation. A nonlinear robust controller is proposed, which consists of an attitude controller to stabilize the rotational motions and a position controller to control translational motions. The quadrotor dynamics involves uncertainties such as parameter uncertainties, nonlinearities, and external disturbances and their effects on closed-loop control system can be guaranteed to be restrained. Simulation results on the quadrotor demonstrate the effectiveness of the designed control approach.
基金Project supported by the National Science Foundation (No.DMS-0608984)the Office of Naval Research(No.N00014-06-1-0286)
文摘The recently developed short-time linear response algorithm,which predicts the response of a nonlinear chaotic forced-dissipative system to small external perturbation,yields high precision of the response prediction.However,the computation of the short-time linear response formula with the full rank tangent map can be expensive.Here,a numerical method to potentially overcome the increasing numerical complexity for large scale models with many variables by using the reduced-rank tangent map in the computation is proposed.The conditions for which the short-time linear response approximation with the reduced-rank tangent map is valid are established,and two practical situations are examined,where the response to small external perturbations is predicted for nonlinear chaotic forced-dissipative systems with different dynamical properties.
基金Supported by the National Natural Science Foundation of China under Grant No.11071164Innovation Program of Shanghai Municipal Education Commission under Grant Nos.12YZ105 and 13ZZ118+1 种基金the Foundation of University Young Teachers Training Program of Shanghai Municipal Education Commission under Grant No.slg11029the National Natural Science Foundation of China under Grant No.11171220
文摘In this paper,the rogue waves of the higher-order dispersive nonlinear Schrdinger(HDNLS) equation are investigated,which describes the propagation of ultrashort optical pulse in optical fibers.The rogue wave solutions of HDNLS equation are constructed by using the modified Darboux transformation method.The explicit first and secondorder rogue wave solutions are presented under the plane wave seeding solution background.The nonlinear dynamics and properties of rogue waves are discussed by analyzing the obtained rational solutions.The influence of little perturbation on the rogue waves is discussed with the help of graphical simulation.
文摘The paper addresses the system performance of coal-fired power unit with changed auxiliary system or other local heat disturbance. The idea of state space model is imported and the universal formula for the calculation of system performance output is deduced on the system state equation. Two important vector of system are worked out under linear system assumption and transform. The transfer matrix is the characteristics of system itself and is constant for a similar condition, which greatly facilitates the analysis. The concept of thermal disturbance vector is proposed to construct the thermal disturbance input easily. The method can be helpful for analyzing any thermal disturbance input satisfying the assumption and also for supplementing the correction means of performance test. An example of 600MW power unit is presented to demonstrate its availability.
文摘The dynamical behaviors of a two-species discrete ratio-dependent predator-prey sys- tem are considered. Some sufficient conditions for the local stability of the equilibria is obtained by using the linearization method. Further, we also obtain a new sufficient condition to ensure that the positive equilibrium is globally asymptotically stable by using an iteration scheme and the comparison principle of difference equations, which generalizes what paper [G. Chen, Z. Teng and Z. Hu, Analysis of stability for a discrete ratio-dependent predator-prey system, Indian J. Pure Appl. Math. 42（1） （2011） 1-26] has done. The method given in this paper is new and very resultful comparing with papers [H. F. Huo and W. T. Li, Existence and global stability of periodic solutions of a discrete predator--prey system with delays, Appl. Math. Comput. 153 （2004） 337-351; X. Liao, S. Zhou and Y. Chen, On permanence and global stability in a general Gilpin- Ayala competition predator prey discrete system, Appl. Math. Comput. 190 （2007） 500-509] and it can also be applied to study the global asymptotic stability for general multiple species discrete population systems. At the end of this paper, we present an open question.
文摘The paper presents the formulation to compute numerically the unsteady aerodynamic forces on the vibrating annular cascade blades.The formulation is based on the finite volume method.By applying the TVD scheme to the linear unsteady calculations,the precise calculation of the peak of unsteady aerodynamic forces at the shock wave location like the delta function singularity becomes possible without empirical constants.As a further feature of the present paper,results of the present numerical calculation are compared with those of the double linearization theory(DLT),which assumes small unsteady and steady disturbances but the unsteady disturbances are much smaller than the steady disturbances.Since DLT requires far less computational resources than the present numerical calculation,the validation of DLT is quite important from the engineering point of view.Under the conditions of small steady disturbances,a good agreement between these two results is observed,so that the two codes are cross-validated.The comparison also reveals the limitation on the applicability of DLT.
文摘In this paper the liquid argon nanojet break-up phenomenon was studied using the molecular dynamics method. The effects of temperature, nozzle diameter and body force on the nanojet break-up length and time were simu- lated. Meanwhile, the particle size, wave length and the frequency of the disturbance were compared with the re- suits of linear stability analysis. The results showed that even though the fluid becomes discontinuous, the tradi- tional linear stability analysis can be used to make a rough calculation of the nanojet break-up.
基金supported by the Project of National Natural Science Foundation of China for Innovation Research Group (Grant No. 51421004)the National Natural Science Foundation of China (Grant No. 51275384)China Postdoctoral Science Foundation (Grant No. 2014M560765)
文摘A general and efficient method is presented in this paper for studying the effects of unbalance on the breathing mechanism of crack.Based on 3D finite element models combined with a nonlinear contact approach for crack modeling, the method is free from theassumption of weight-dominance and can be used to gain deep insights into the breathing mechanism of crack. In order to greatlyreduce the computational time, a complex free-interface component mode synthesis (CMS) method is employed to reduce theorder of the model. Based on the proposed method, the effects of unbalance on the breathing mechanism of crack are discussed.Numerical results show that the unbalance can lead to significant changes in the breathing of crack, even when the unbalance force is about an order of magnitude smaller than the self-weight. Moreover, the level and orientation of the unbalance have also remarkable effects on the breathing behaviors of crack. Besides, a new universal non-steady breathing phenomenon of crack is firstly found in this paper, which denotes that the breathing speed of a crack is fluctuated over one revolution when there exists residual unbalance in the cracked rotor.
