The parabolized stability equations (PSEs) for high speed flows, especially supersonic and hypersonic flows, are derived and used to analyze the nonparallel boundary layer stability. The proposed numerical technique...The parabolized stability equations (PSEs) for high speed flows, especially supersonic and hypersonic flows, are derived and used to analyze the nonparallel boundary layer stability. The proposed numerical techniques for solving PSE include the following contents: introducing the efficiently normal transformation of the boundary layer, improving the computational accuracy by using a high-order differential scheme near the wall, employing the predictor-corrector and iterative approach to satisfy the important normalization condition, and implementing the stable spatial marching. Since the second mode dominates the growth of the disturbance in high Mach number flows, it is used in the computation. The evolution and characteristics of the boundary layer stability in the high speed flow are demonstrated in the examples. The effects of the nonparallelizm, the compressibility and the cooling wall on the stability are analyzed. And computational results are in good agreement with the relevant data.展开更多
The approximate expressions of the travelling wave solutions for a class of nonlinear disturbed long-wave system are constructed using the generalized variational iteration method.
A new type of shear viscous damper for rotating machinery is designed. The new damper with good stability and reliability can inhibit all kinds of frequency multiplication vibration caused by misalignment in the condi...A new type of shear viscous damper for rotating machinery is designed. The new damper with good stability and reliability can inhibit all kinds of frequency multiplication vibration caused by misalignment in the condition of nonstop machine. It analyzes and discusses the use of the shear viscous damper for misalignment vibration response inhibition with a finite element method, and experi ments are extensively carried out with a laboratory test rig. Both the simulation and experimental re suits basically agree well in that, the damper can effectively control the misalignment vibration of the rotor system and improves the stability of the plitude of one time running speed component bration has been basically eliminated. entire rotor system. Experimental results show the am decreases by 30% , and the two time running speed vibration has been basically eliminated.展开更多
In this paper, we introduce a modified small-world network added with new links with preferential connection instead of adding randomly, then we apply Bak-Sneppen (BS) evolution model on this network. Several dynami...In this paper, we introduce a modified small-world network added with new links with preferential connection instead of adding randomly, then we apply Bak-Sneppen (BS) evolution model on this network. Several dynamical character of the model such as the evolution graph, fo avalanche, the critical exponent D and T, and the distribution of mutation times of all the nodes, show particular behaviors different from those of the model based on the regular network and the small-world network.展开更多
The complex systems approach offers an opportunity to replace the extant pre-dominant mechanistic view on sport-related phenomena.The emphasis on the environment-system relationship,the applications of complexity prin...The complex systems approach offers an opportunity to replace the extant pre-dominant mechanistic view on sport-related phenomena.The emphasis on the environment-system relationship,the applications of complexity principles,and the use of nonlinear dynamics mathematical tools propose a deep change in sport science.Coordination dynamics,ecological dynamics,and network approaches have been successfully applied to the study of different sport-related behaviors,from movement patterns that emerge at different scales constrained by specific sport contexts to game dynamics.Sport benefit from the use of such approaches in the understanding of technical,tactical,or physical conditioning aspects which change their meaning and dilute their frontiers.The creation of new learning and training strategies for teams and individual athletes is a main practical consequence.Some challenges for the future are investigating the influence of key control parameters in the nonlinear behavior of athlete-environment systems and the possible relatedness of the dynamics and constraints acting at different spatio-temporal scales in team sports.Modelling sport-related phenomena can make useful contributions to a better understanding of complex systems and vice-versa.展开更多
In this paper,we investigate nonlinear the perturbed nonlinear Schrdinger's equation (NLSE) with Kerr law nonlinearity given in [Z.Y.Zhang,et al.,Appl.Math.Comput.216 (2010) 3064] and obtain exact traveling soluti...In this paper,we investigate nonlinear the perturbed nonlinear Schrdinger's equation (NLSE) with Kerr law nonlinearity given in [Z.Y.Zhang,et al.,Appl.Math.Comput.216 (2010) 3064] and obtain exact traveling solutions by using infinite series method (ISM),Cosine-function method (CFM).We show that the solutions by using ISM and CFM are equal.Finally,we obtain abundant exact traveling wave solutions of NLSE by using Jacobi elliptic function expansion method (JEFEM).展开更多
This paper is concerned with the kinematic nonlinearity measure of parallel kinematic machine tool (PKM), which depends upon differential geometry curvalure. The nonlinearity can be described by the curve of the solut...This paper is concerned with the kinematic nonlinearity measure of parallel kinematic machine tool (PKM), which depends upon differential geometry curvalure. The nonlinearity can be described by the curve of the solution locus and the equal interval input of joints mapping into inequable interval output of the end-effectors. Such curing and inequation can be measured by BW curvature. So the curvature can measure the nonlinearity of PKM indirectly. Then the distribution of BW curvature in the local area and the whole workspace are also discussed. An example of application to the interpolation accuracy analysis of PKM is given to illustrate the effectiveness of this approach.展开更多
The flutter, post-flutter and active control of a two-dimensional airfoil with control surface operating in supersonic/hypersonic flight speed regions are investigated in this paper. A three-degree-of-freedom dynamic ...The flutter, post-flutter and active control of a two-dimensional airfoil with control surface operating in supersonic/hypersonic flight speed regions are investigated in this paper. A three-degree-of-freedom dynamic model is established, in which both the cubic nonlinear structural stiffness and the nonlinear aerodynamic load are accounted for. The third order Piston Theory is employed to derive the aerodynamic loads in the supersonic/hypersonic airflow. Nonlinear flutter happens with a phenomenon of limit cycle oscillations (LCOs) when the flight speed is less than or greater than linear critical speed. The LQR approach is employed to design a control law to increase both the linear and nonlinear critical speeds of aerodynamic flutter, and then a combined control law is proposed in order to reduce the amplitude of LCOs by adding a cubic nonlinear feedback control. The dynamic responses of the controlled system are given and used to compare with those of the uncontrolled system. Results of simulation show that the active flutter control method proposed here is effective.展开更多
The design of the re-entry space vehicles and high-speed aircraft structures requires special attention to the non-linear thermoelastic and aerodynamic instabilities.The thermal effects are important since temperature...The design of the re-entry space vehicles and high-speed aircraft structures requires special attention to the non-linear thermoelastic and aerodynamic instabilities.The thermal effects are important since temperature environment influences significantly the static and dynamic behaviors of flight structures in supersonic/hypersonic regimes.The dynamic behavior of a double-wedge lifting surface with combined freeplay and cubic stiffening structural nonlinearities in both plunging and pitching degrees-of-freedom(DOF) operating in supersonic/hypersonic flight speed regimes has been analyzed.In addition a third order piston theory aerodynamics(PTA) is used to evaluate the non-linear unsteady aerodynamic loads applied to the wing section.Loss of torsional stiffness that may be incurred by lifting surfaces subjected to axial stresses induced by aerodynamic heating is also considered.The aerodynamic heating effect is estimated based on the adiabatic wall temperature due to high speed airstreams.It is demonstrated that serious losses of torsional stiffness may occur in such lifting surfaces;the influence of various parameters such as flight condition,thickness ratio,freeplays and pitching stiffness nonlinearity are discussed.展开更多
This article amis at revealing dynamical behavior of a coupled Camassa–Holm type equation, which was proposed by Geng and Wang based on a 4×4 matrix spectral problem with two potentials. Its kink and anti-kink s...This article amis at revealing dynamical behavior of a coupled Camassa–Holm type equation, which was proposed by Geng and Wang based on a 4×4 matrix spectral problem with two potentials. Its kink and anti-kink solutions are presented explicitly. In particular, some exact multi-kink and anti-kink wave solutions are discussed and under some conditions, the kink and anti-kinks look like hat-shape solitons. The dynamic characters of the obtained solutions are investigated by figures. The method used in this paper can be widely applied to looking for the multi-kinks for Camassa–Holm type equations possessing cubic nonlinearity.展开更多
The aeroelastic responses of a high-aspect-ratio wing are investigated based on nonlinear experimental aerodynamic forces. The influences of nonlinear experimental aerodynamic forces and dynamic pressures on the wing ...The aeroelastic responses of a high-aspect-ratio wing are investigated based on nonlinear experimental aerodynamic forces. The influences of nonlinear experimental aerodynamic forces and dynamic pressures on the wing loads are studied in the longitudinal and lateral maneuver states. The flight loads of the wing fixed at the root are calculated at different angles of attack. The aileron efficiency with respect to the dynamic pressures and aileron deflections are also studied. The results indicate that the flight loads of the wings vary nonlinearly with the angle of attack and dynamic pressure. Due to the high-lift aerofoil, elastic components are a large portion of the wing loads, especially for small angles of attack and high dynamic pressure condi-tions. The aileron efficiency is significantly affected by aileron deflections, dynamic pressures and angles of attack when the nonlinear experimental aerodynamic forces are used for calculation. In states with high dynamic pressures and large aileron deflections, aileron reversal can occur. The aileron deflection and angle of attack have a nonlinear effect on the aileron efficiency. An efficient method for analyzing the flight loads and structural design of high-aspect-ratio wings is derived in this study, and the analysis can provide insight into the distribution of flight loads for high-aspect-ratio wings.展开更多
This paper considers the combined effects of the nonlinear intra-specific regulation and maturation delays on the two-species competition model. Dynamical behaviors of the model are studied, and sharp global asymptoti...This paper considers the combined effects of the nonlinear intra-specific regulation and maturation delays on the two-species competition model. Dynamical behaviors of the model are studied, and sharp global asymptotical stability criteria for the coexistence equilibrium as well as the excluding equilibria are established. It is shown that increase of the maturation delay of one species has negative effect on its permanence and a sufficiently large maturation delay will directly lead to its extinction, and that variation of the intra-specific regulation parameter of one species may change the surviving or extinction behaviors of its competitor.展开更多
The suspension of electrodynamic loudspeakers includes a surround of the cone and a spider, and it is characterized by the mechanic stiffness in the lumped-parameter model. By solving the nonlinear differential equati...The suspension of electrodynamic loudspeakers includes a surround of the cone and a spider, and it is characterized by the mechanic stiffness in the lumped-parameter model. By solving the nonlinear differential equation of motion which considers the nonlinearity of suspension at low frequencies numerically and measuring different kinds of surrounds and spiders, the nonlinear behavior of suspension is theoretically and experimentally studied. Since the nonlinear stiffness of spiders and surrounds can be measured and fitted respectively before assembled into loudspeakers, which spider works best with which surround is studied. The performance of loudspeakers such as harmonic distortion based on the nonlinear parameters can be predicted.展开更多
This paper addresses the problem of synchronized path following of multiple homogenous underaetuated autonomous underwater vehicles (AUVs). The dedicated control laws are categorized into two envelopes: One is stee...This paper addresses the problem of synchronized path following of multiple homogenous underaetuated autonomous underwater vehicles (AUVs). The dedicated control laws are categorized into two envelopes: One is steering individual underwater vehicle to track along predefined path, and the other is ensuring tracked paths of multiple vehicles to be synchronized, by means of decentralized speed adaption under the constraints of multi-vehicle communication topology. With these two tasks formulation, geometric path following is built on Lyapunov theory and baekstepping techniques, while injecting helmsman behavior into classic individual path following control. Synchronization of path parameters are reached by using a mixture of tools from linear algebra, graph theory and nonlinear control theory. A simple but effective control design on direct inter-vehicle speed adaption with minimized communication variables, enables the multi-AUV systems to be synchronized and stabilized into an invariant manifold, and all speeds converge to desired assignments as a byproduct. Simulation results illustrate the performance of the synchronized path following control laws proposed.展开更多
The exact explicit traveling solutions to the two completely integrable sixthorder nonlinear equations KdV6 are given by using the method of dynamical systems and Cosgrove's work.It is proved that these traveling ...The exact explicit traveling solutions to the two completely integrable sixthorder nonlinear equations KdV6 are given by using the method of dynamical systems and Cosgrove's work.It is proved that these traveling wave solutions correspond to some orbits in the 4-dimensional phase space of two 4-dimensional dynamical systems.These orbits lie in the intersection of two level sets defined by two first integrals.展开更多
We discuss the nonlinear Schr6dinger equation with variable coefficients in 21) graded-index waveguides with different distributed transverse diffractions and obtain exact bright and dark soliton solutions. Based on ...We discuss the nonlinear Schr6dinger equation with variable coefficients in 21) graded-index waveguides with different distributed transverse diffractions and obtain exact bright and dark soliton solutions. Based on these solutions, we mainly investigate the dynamical behaviors of solitons in three different diffraction decreasing waveguides with the hyperbolic, Gaussian and Logarithmic profiles. Results indicate that for the same parameters, the amplitude of bright solitons in the Logarithmic profile and the amplitude of dark solitons in the Gaussian profile are biggest respectively, and the amplitude in the hyperbolic profile is smallest, while the width of solitons has the opposite case.展开更多
A nonlinear dynamical system is proposed as a qualitative mathematical model with the twofold aim to reasonably describe the force behavior in a fatiguing sub-maximal contraction and to be possibly employed in assessi...A nonlinear dynamical system is proposed as a qualitative mathematical model with the twofold aim to reasonably describe the force behavior in a fatiguing sub-maximal contraction and to be possibly employed in assessing muscular activation indexes. The model's properties are studied in terms of its equilibria and their stability properties and the existence of the fatigue equilibrium is ensured as the only system's attractor in the feasibility range of the parameters. Suitable mathematical indicators -- related to the dynamical properties of resilience and reactivity -- are introduced to characterize the asymptotic and the transient system's behavior. The practical impact of the analytical results is elucidated and a connection is established between the introduced mathematical indicators and muscle functionality indexes as rate of force development, task failure time and complete restore time. Experimental validation with handgrip force signal at high load and possible practical applications are also presented.展开更多
The integrable nonlocal Lakshmanan–Porsezian–Daniel(LPD) equation which has the higher-order terms(dispersions and nonlinear effects) is first introduced. We demonstrate the integrability of the nonlocal LPD equatio...The integrable nonlocal Lakshmanan–Porsezian–Daniel(LPD) equation which has the higher-order terms(dispersions and nonlinear effects) is first introduced. We demonstrate the integrability of the nonlocal LPD equation,provide its Lax pair, and present its rational soliton solutions and self-potential function by using the degenerate Darboux transformation. From the numerical plots of solutions, the compression effects of the real refractive index profile and the gain-or-loss distribution produced by δ are discussed.展开更多
文摘The parabolized stability equations (PSEs) for high speed flows, especially supersonic and hypersonic flows, are derived and used to analyze the nonparallel boundary layer stability. The proposed numerical techniques for solving PSE include the following contents: introducing the efficiently normal transformation of the boundary layer, improving the computational accuracy by using a high-order differential scheme near the wall, employing the predictor-corrector and iterative approach to satisfy the important normalization condition, and implementing the stable spatial marching. Since the second mode dominates the growth of the disturbance in high Mach number flows, it is used in the computation. The evolution and characteristics of the boundary layer stability in the high speed flow are demonstrated in the examples. The effects of the nonparallelizm, the compressibility and the cooling wall on the stability are analyzed. And computational results are in good agreement with the relevant data.
基金*Supported by the National Natural Science Foundation of China under Grant No. 40876010, the Main Direction Program of the Knowledge Innovation Project of Chinese Academy of Sciences under Grant No. KZCX2-YW-Q03-08, the R &: D Special Fund for Public Welfare Industry (Meteorology) under Grant No. GYHY200806010, the LASG State Key Laboratory Special Fund and the Foundation of E-Institutes of Shanghai Municipal Education Commission (E03004)
文摘The approximate expressions of the travelling wave solutions for a class of nonlinear disturbed long-wave system are constructed using the generalized variational iteration method.
基金Supported by the National Basic Research Program of China(No.2012CB026000)the Joint Project Special Fund of Education Committee of Beijingthe Ph.D.Programs Foundation of Ministry of Education of China(No.20110010110009)
文摘A new type of shear viscous damper for rotating machinery is designed. The new damper with good stability and reliability can inhibit all kinds of frequency multiplication vibration caused by misalignment in the condition of nonstop machine. It analyzes and discusses the use of the shear viscous damper for misalignment vibration response inhibition with a finite element method, and experi ments are extensively carried out with a laboratory test rig. Both the simulation and experimental re suits basically agree well in that, the damper can effectively control the misalignment vibration of the rotor system and improves the stability of the plitude of one time running speed component bration has been basically eliminated. entire rotor system. Experimental results show the am decreases by 30% , and the two time running speed vibration has been basically eliminated.
基金The project supported by National Natural Science Foundation of China under Grant No. 90203008 and the Doctoral Foundation of the Ministry of Education of China under Grant No. 2002055009
文摘In this paper, we introduce a modified small-world network added with new links with preferential connection instead of adding randomly, then we apply Bak-Sneppen (BS) evolution model on this network. Several dynamical character of the model such as the evolution graph, fo avalanche, the critical exponent D and T, and the distribution of mutation times of all the nodes, show particular behaviors different from those of the model based on the regular network and the small-world network.
文摘The complex systems approach offers an opportunity to replace the extant pre-dominant mechanistic view on sport-related phenomena.The emphasis on the environment-system relationship,the applications of complexity principles,and the use of nonlinear dynamics mathematical tools propose a deep change in sport science.Coordination dynamics,ecological dynamics,and network approaches have been successfully applied to the study of different sport-related behaviors,from movement patterns that emerge at different scales constrained by specific sport contexts to game dynamics.Sport benefit from the use of such approaches in the understanding of technical,tactical,or physical conditioning aspects which change their meaning and dilute their frontiers.The creation of new learning and training strategies for teams and individual athletes is a main practical consequence.Some challenges for the future are investigating the influence of key control parameters in the nonlinear behavior of athlete-environment systems and the possible relatedness of the dynamics and constraints acting at different spatio-temporal scales in team sports.Modelling sport-related phenomena can make useful contributions to a better understanding of complex systems and vice-versa.
基金Supported by the Research Foundation of Education Bureau of Hunan Province under Grant No.11C0628Foundation of Hunan Institute of Science and Technology under Grant No.2011Y49
文摘In this paper,we investigate nonlinear the perturbed nonlinear Schrdinger's equation (NLSE) with Kerr law nonlinearity given in [Z.Y.Zhang,et al.,Appl.Math.Comput.216 (2010) 3064] and obtain exact traveling solutions by using infinite series method (ISM),Cosine-function method (CFM).We show that the solutions by using ISM and CFM are equal.Finally,we obtain abundant exact traveling wave solutions of NLSE by using Jacobi elliptic function expansion method (JEFEM).
基金This work was supported by the National Natural Science Foundation of China (Grant No. 59805011) the National 973 Program (G1998030607) the National 863 High-Tech Development Program (863-511-943-001).
文摘This paper is concerned with the kinematic nonlinearity measure of parallel kinematic machine tool (PKM), which depends upon differential geometry curvalure. The nonlinearity can be described by the curve of the solution locus and the equal interval input of joints mapping into inequable interval output of the end-effectors. Such curing and inequation can be measured by BW curvature. So the curvature can measure the nonlinearity of PKM indirectly. Then the distribution of BW curvature in the local area and the whole workspace are also discussed. An example of application to the interpolation accuracy analysis of PKM is given to illustrate the effectiveness of this approach.
基金supported by the National Natural Science Foundation of China (Grant Nos. 90816002 and 10772056)the Astronautics Technology Foundation, the Ministry of Information and Industry of China (Grant No. 2009-HT-HGD-07)
文摘The flutter, post-flutter and active control of a two-dimensional airfoil with control surface operating in supersonic/hypersonic flight speed regions are investigated in this paper. A three-degree-of-freedom dynamic model is established, in which both the cubic nonlinear structural stiffness and the nonlinear aerodynamic load are accounted for. The third order Piston Theory is employed to derive the aerodynamic loads in the supersonic/hypersonic airflow. Nonlinear flutter happens with a phenomenon of limit cycle oscillations (LCOs) when the flight speed is less than or greater than linear critical speed. The LQR approach is employed to design a control law to increase both the linear and nonlinear critical speeds of aerodynamic flutter, and then a combined control law is proposed in order to reduce the amplitude of LCOs by adding a cubic nonlinear feedback control. The dynamic responses of the controlled system are given and used to compare with those of the uncontrolled system. Results of simulation show that the active flutter control method proposed here is effective.
基金the China Post Doctor National Fund (No.AD4122,2008)
文摘The design of the re-entry space vehicles and high-speed aircraft structures requires special attention to the non-linear thermoelastic and aerodynamic instabilities.The thermal effects are important since temperature environment influences significantly the static and dynamic behaviors of flight structures in supersonic/hypersonic regimes.The dynamic behavior of a double-wedge lifting surface with combined freeplay and cubic stiffening structural nonlinearities in both plunging and pitching degrees-of-freedom(DOF) operating in supersonic/hypersonic flight speed regimes has been analyzed.In addition a third order piston theory aerodynamics(PTA) is used to evaluate the non-linear unsteady aerodynamic loads applied to the wing section.Loss of torsional stiffness that may be incurred by lifting surfaces subjected to axial stresses induced by aerodynamic heating is also considered.The aerodynamic heating effect is estimated based on the adiabatic wall temperature due to high speed airstreams.It is demonstrated that serious losses of torsional stiffness may occur in such lifting surfaces;the influence of various parameters such as flight condition,thickness ratio,freeplays and pitching stiffness nonlinearity are discussed.
基金Supported by the National Natural Science Foundation of China under Grant No.11261037the Natural Science Foundation of Inner Mongolia Autonomous Region under Grant No.2014MS0111+1 种基金the Caoyuan Yingcai Program of Inner Mongolia Autonomous Region under Grant No.CYYC2011050the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region under Grant No.NJYT14A04
文摘This article amis at revealing dynamical behavior of a coupled Camassa–Holm type equation, which was proposed by Geng and Wang based on a 4×4 matrix spectral problem with two potentials. Its kink and anti-kink solutions are presented explicitly. In particular, some exact multi-kink and anti-kink wave solutions are discussed and under some conditions, the kink and anti-kinks look like hat-shape solitons. The dynamic characters of the obtained solutions are investigated by figures. The method used in this paper can be widely applied to looking for the multi-kinks for Camassa–Holm type equations possessing cubic nonlinearity.
基金supported by the National Natural Science Foundation of China (Grant Nos. 60736025, 90716006, 10902006)the Doctoral Pro-gram Foundation of Institutions of Higher Education of China (Grant No. 20091102110015)the Major Programs of China National Space Administration (Grant No. D2120060013)
文摘The aeroelastic responses of a high-aspect-ratio wing are investigated based on nonlinear experimental aerodynamic forces. The influences of nonlinear experimental aerodynamic forces and dynamic pressures on the wing loads are studied in the longitudinal and lateral maneuver states. The flight loads of the wing fixed at the root are calculated at different angles of attack. The aileron efficiency with respect to the dynamic pressures and aileron deflections are also studied. The results indicate that the flight loads of the wings vary nonlinearly with the angle of attack and dynamic pressure. Due to the high-lift aerofoil, elastic components are a large portion of the wing loads, especially for small angles of attack and high dynamic pressure condi-tions. The aileron efficiency is significantly affected by aileron deflections, dynamic pressures and angles of attack when the nonlinear experimental aerodynamic forces are used for calculation. In states with high dynamic pressures and large aileron deflections, aileron reversal can occur. The aileron deflection and angle of attack have a nonlinear effect on the aileron efficiency. An efficient method for analyzing the flight loads and structural design of high-aspect-ratio wings is derived in this study, and the analysis can provide insight into the distribution of flight loads for high-aspect-ratio wings.
文摘This paper considers the combined effects of the nonlinear intra-specific regulation and maturation delays on the two-species competition model. Dynamical behaviors of the model are studied, and sharp global asymptotical stability criteria for the coexistence equilibrium as well as the excluding equilibria are established. It is shown that increase of the maturation delay of one species has negative effect on its permanence and a sufficiently large maturation delay will directly lead to its extinction, and that variation of the intra-specific regulation parameter of one species may change the surviving or extinction behaviors of its competitor.
基金supported by the National Natural Science Foundation of China(Grant No. 11274172)
文摘The suspension of electrodynamic loudspeakers includes a surround of the cone and a spider, and it is characterized by the mechanic stiffness in the lumped-parameter model. By solving the nonlinear differential equation of motion which considers the nonlinearity of suspension at low frequencies numerically and measuring different kinds of surrounds and spiders, the nonlinear behavior of suspension is theoretically and experimentally studied. Since the nonlinear stiffness of spiders and surrounds can be measured and fitted respectively before assembled into loudspeakers, which spider works best with which surround is studied. The performance of loudspeakers such as harmonic distortion based on the nonlinear parameters can be predicted.
基金supported by the EU FP6 FreeSubNet project under Grant No.036186the National Science Foundation of China under Grant No.51079061+1 种基金the Key Laboratory of Education Ministry for Image Processing and Intelligent Control,Huazhong University of Science and Technology under Grant No. 200804supported by the European Marie Curie Fellowship
文摘This paper addresses the problem of synchronized path following of multiple homogenous underaetuated autonomous underwater vehicles (AUVs). The dedicated control laws are categorized into two envelopes: One is steering individual underwater vehicle to track along predefined path, and the other is ensuring tracked paths of multiple vehicles to be synchronized, by means of decentralized speed adaption under the constraints of multi-vehicle communication topology. With these two tasks formulation, geometric path following is built on Lyapunov theory and baekstepping techniques, while injecting helmsman behavior into classic individual path following control. Synchronization of path parameters are reached by using a mixture of tools from linear algebra, graph theory and nonlinear control theory. A simple but effective control design on direct inter-vehicle speed adaption with minimized communication variables, enables the multi-AUV systems to be synchronized and stabilized into an invariant manifold, and all speeds converge to desired assignments as a byproduct. Simulation results illustrate the performance of the synchronized path following control laws proposed.
基金Project supported by the National Natural Science Foundation of China (Nos.10771196,10831003)the Innovation Project of Zhejiang Province (No.T200905)
文摘The exact explicit traveling solutions to the two completely integrable sixthorder nonlinear equations KdV6 are given by using the method of dynamical systems and Cosgrove's work.It is proved that these traveling wave solutions correspond to some orbits in the 4-dimensional phase space of two 4-dimensional dynamical systems.These orbits lie in the intersection of two level sets defined by two first integrals.
基金Supported by the Higher School Visiting Scholar Development Project under Grant No.FX2013103the Research Fund under Grant No.ZCI2XJY003+2 种基金 Research Fund for the Doctoral Program under Grant No.Z301B13519 of the Zhejiang University of Media and CommunicationsZhejiang Province Science Foundation for Youths under Grant No.LQ12F05005National Natural Science Foundation of China under Grant No.11374254
文摘We discuss the nonlinear Schr6dinger equation with variable coefficients in 21) graded-index waveguides with different distributed transverse diffractions and obtain exact bright and dark soliton solutions. Based on these solutions, we mainly investigate the dynamical behaviors of solitons in three different diffraction decreasing waveguides with the hyperbolic, Gaussian and Logarithmic profiles. Results indicate that for the same parameters, the amplitude of bright solitons in the Logarithmic profile and the amplitude of dark solitons in the Gaussian profile are biggest respectively, and the amplitude in the hyperbolic profile is smallest, while the width of solitons has the opposite case.
文摘A nonlinear dynamical system is proposed as a qualitative mathematical model with the twofold aim to reasonably describe the force behavior in a fatiguing sub-maximal contraction and to be possibly employed in assessing muscular activation indexes. The model's properties are studied in terms of its equilibria and their stability properties and the existence of the fatigue equilibrium is ensured as the only system's attractor in the feasibility range of the parameters. Suitable mathematical indicators -- related to the dynamical properties of resilience and reactivity -- are introduced to characterize the asymptotic and the transient system's behavior. The practical impact of the analytical results is elucidated and a connection is established between the introduced mathematical indicators and muscle functionality indexes as rate of force development, task failure time and complete restore time. Experimental validation with handgrip force signal at high load and possible practical applications are also presented.
基金Supported by the National Natural Science Foundation of China under Grant No.11271210the K.C.Wong Magna Fund in Ningbo University
文摘The integrable nonlocal Lakshmanan–Porsezian–Daniel(LPD) equation which has the higher-order terms(dispersions and nonlinear effects) is first introduced. We demonstrate the integrability of the nonlocal LPD equation,provide its Lax pair, and present its rational soliton solutions and self-potential function by using the degenerate Darboux transformation. From the numerical plots of solutions, the compression effects of the real refractive index profile and the gain-or-loss distribution produced by δ are discussed.