Abstract:The inverse problem of the calculus of variations for the firstorder system was restudied. The errors on the conditions of selfadjointness for a system of the firstorder ordinary differential equations in some literatures were amend. The equations to determine the matrices of the selfadoint transformations for the firstorder system were obtained. Two methods of constraction of the Lagrangians for the firstorder selfadjoint system were presented. An example was given to illustrate the application of the result.

Abstract:An improved homotopy analysis method with two auxiliary parameters was introduced, then the homotopy approximate solutions for the generalized KuramotoSivashinsky equation were obtained by using this method. which were compared with the exact solitary wave solutions. And the comparison shows that the approximate solution more effectively approaches the real solution, because it contains two auxiliary parameters, which can regulate and control more effectively its convergence region and rate. This indicates that the improved homotopy analysis method with two auxiliary parameters has its advantages to study complex nonlinear systems.

Abstract:The instability of a twodimensional thin panel in subsonic flow was studied by using Differential Quadrature Method (DQ method). The eigenvalue numeric method was used to study the instability characteristics of panels with differential boundary conditions. The results show: 1) that the critical parameters can be efficiently obtained by DQ method;2) that panel which is fixed at both ends undergoes divergence;3) that the clampedspring support panel flutters,4) and that the critical flutter dynamic pressure is influenced by some system parameters.

Abstract:A method of initialvalue transformation was presented to obtain the approximate analytic periods of a class of nonlinear oscillators. The periodic solutions can be expressed in the forms of basic harmonics and bifurcate harmonics. Thus, an oscillation system, which is described as a second order ordinary differential equation, can be expressed as a set of nonlinear algebraic equations with a frequency, amplitudes as the independent variables using RitzGalerkin’s method. But the set of equations is incomplete, and the key is to consider initial value transformation. After adding supplementary equations, a set of nonlinear algebraic equations with angular frequencies, amplitudes as the independent variables was constituted completely. For examples, six asymmetric periodic solutions bifurcating about a nonlinear differential equation arising in general relativity were solved by using the method of initialvalue transform. Amplitudefrequency curves and central offsetfrequency curves of the asymmetrically vibration systems were derived. In addition, the drift phenomenon of natural angular frequency was discovered.

Abstract:A discrete finitedimensional dynamical model was built to describe the space large overall motion of tethered satellite system with an infinitedimensional viscoelastic tether in a long time. The tethered satellite system is a complex nolinear dynamic system. Considering the tether’s viscoelasticity, distributed mass and space form, the established improved bead model can meticulously describe the tether’s vertical and horizontal vibration. According to tether’s characteristic of tensile and not compressive, the slack tether unit model was set up to accurately reflect real stress of tether. The determination of the number of degreesoffreedom of the system was studied. Based on numerical integral calculation, the dynamic response was obtained via numerical simulation of the deployment, retrievement and retainment process of tethered satellite system in a long time. The result is convergent. The simulation proves the important role of the stable equilibrium position in the dynamics of tethered space system.

Abstract:This paper was concerned with the synchronization of discrete chaotic systems with parameter uncertainties. The TakagiSugeno(TS) fuzzy impulsive control model for discrete chaotic systems with parameter uncertainties was established via the TS modeling technique and impulsive technique. Based on the new model, a sufficient control condition for discrete chaotic systems with parameter uncertainties has been derived by matrix analysis and Lyapunov theory. An illustrative example was given to show the effectiveness of the results. Compared with the existing results, the obtained results exhibit certain advantage.

Abstract:This paper investigated the adaptive synchronization of a driveresponse dynamical network, in which each node is a chaotic system with unkonwn parameters. Based on the Lyapunov stability theory and LaSalle’s invariant set theory, suitable controllers and parameters update laws were designed to achieve synchronization between the drive system and response dynamical network. A weighted network and a scalefree network were used as examples to verify theoretical results. In addition, with the same network topology, synchronization time of different dynamics was compared. Numerical simulations show the effectiveness of the control scheme.

Abstract:For a chaotic system with unknown amplitude and frequency in external exciting force, the unknown parameters were expanded to be the new state vector and a new drive system was constructed. By a parametric adaptive control, a response system with the same structure as the drive system was constructed. Based on the stability theory in the cascade system, controllers and the parametric adaptive law were designed by two steps, which make the driveresponse systems achieve complete synchronization. Then the unknown amplitude and frequency of the drive system can be identified. The forced DuffingVan der Pol oscillator and loudspeaker system were taken as examples to illustrate the effectiveness of the proposed method.

Abstract:Based on the chaos synchronization control theory research, and combined with the simultaneous control and linear feedback control method, this paper put forward a control strategy for the synchronization of different structure hyperchaotic system. On the basis of Chua chaos system and Chen chaos system theory research, two different structure five order chaotic systems were obtained by adding two feedback controllers, and the dynamics analysis confirmed that they were the fifthorder hyperchaotic system, whose plane phase diagrams were obtained by numerical simulation in Mathmatic environment. By adopting the Full State Hybird Projective Synchronization, their simultaneous synchronization control can be achieved, and the Runge Kutta algorithm was used to numerically simulate, the control, which confirmed that the synchronization method was effective and feasible.

Abstract:The adaptiveimpulsive control strategy is used to realize the synchronization of a complex network coupled with output. The suitable adaptiveimpulsive controller is designed by constructing Lyapunov function. Some generic criteria for synchronization are established based on the theory of impulsive differential equation. The criteria guarantee that the dynamical network asymptotically synchronizes at the individual node state in arbitrary specified network. Numerical simulations show the effectiveness of the proposed controllers.

Abstract:The static equilibrium equation of a functionally graded circular plate was established by using elastic theory, and the neutral plane site of the functionally graded circular plate was determined. On this basis, the nonlinear vibration and buckling differential equations for the functionally graded circular plate in uniform temperature field were derived,the approximate solution to nonlinear thermal vibration and buckling of the functionally graded circular plate was obtained, the effects of neutral plane site, gradient index and temperature on nonlinear thermal vibration and buckling of the functionally graded circular plate were discussed and analyzed. The comparison of the calculation results by this method with these by finite element method verified the method was correct. Analysis on examples indicates that the neutral plane site has certain influence on nonlinear thermal vibration and buckling of the functionally graded circular plate in uniform temperature field.

Abstract:In order to obtain the dynamic response of a beam subjected to a moving mass, Its numerical model of spacetime finite element method was established. Considering the inertial terms of a travelling mass, the timevaries different equation of beam under a mass was presented by using. the spacetime finite element method. The characteristic matrices of the discrete element of the BernoulliEuler beam carrying concentrated mass like spacetime inertia and stiffness matrices. Numerical examples by comparing with the results the dynamic response of the beam under the moving mass and the Classical time integration schemes like Newmarkβ and Wilsonθ prove the simplicity and efficiency of the method.

Abstract:A dynamical model of the airfoil with cubic and freeplay nonlinearity in both pitch and plunge was established. The nonlinear aerodynamic force and moment on the wing were evaluated by the third order piston theory. A bifurcation diagram, which presents the relevance between bifurcation parameter and amplitude of the periodic motion, was given numerically. When the dimensionless flight speed increases to the flutter critical speed, limited cycle can be observed in both pitch and plunge, and Hopf bifurcation appears, which means the stable point bifurcates to a periodic motion. And when further increasing the dimensionless flight speed a more complex dynamic phenomenon will turn up .

Abstract:The thermal effects on the kinetics of panel structure were studied. Combining the unsteady aerodynamic model based on sunpersoin piston theory with structural dynamics equation, the flutter equation of thermal panel was obtained. The flutter analysis on thermal panel was carried out by P-K method, and the trend of flow angle on the flutter velocity was discussed. The numerical results show that thermal effect has a great impact on the inherent characteristics of panel,thereby affecting the panel’s flutter characteristic.

Abstract:The spectral element method was applied to analyze and calculate the dynamic response of frame structures. The dynamic stiffness matrices of the bar and beam elements were derived, and the dynamic stiffness matrix for the overall frame structure was assembled. The equations of motion of the overall structure were presented. The natural frequencies and time domain responses were calculated. The present method was compared with the finite element method. The results show that the spectral element method has its unique advantages in terms of numerical simulation.

Abstract:For a certain geometric shape of liquid fuel containerCassini tank, which has a cylindrical waist and two hemispherical bottoms,and is used in a large satellite of our country,the problems of liquid sloshing and lateral forced sloshing in microgravity environment were studied by using finite element method. The finite element equations of the system were derived by means of Galerkin method. The natural frequency of sloshing and the equivalent model parameters of sloshing were obtained. For periodic pulse excitations,the numerical formulations for computing the sloshing force and momentum acting on the wall of the tank were deduced. Finally,the numerical results and some conclusion remarks were given.

Abstract:The effects of the position and size of local defects without diffusion function on patterns of twodimensional random neural network were investigated by using the HodgkinHuxley model. The result shows that the spiral wave becomes more scattered when the size of defect gets bigger, significantly near to the center of the spiral waves, which means the defect impact is correlated with the defect size positively. Furthermore, it is found that the drift phenomenon of spiral wave is induced by defect in weakly coupled neural network. Study on the behavior of spatiotemporal patterns with the coexistence of channel noise and defect shows that the new wave source is made by the effect of noise. Finally, the physical mechanisms for these phenomena were briefly discussed by analyzing the discharge frequency and the mean membrane voltage of neurons.

Abstract:Based on the firing patterns of the nonidentical coupled HindmarshRose neuronal system without timedelay,we numerically studied the effect of timedelay on the bursting patterns when the coupled HindmarshRose neurons obtained almost complete synchronization.The results show that the timedelay makes the firing pattern change, compared with the case without timedelay,and makes the spikes within per busting gradually decrease or almost disappear with the values of delay increasing.The results will help us better understand the important effect of timedelay on the behavior of the coupled neural systems.

Abstract:The dynamics of a twodimensional neural map subjected to two harmonic signals with different frequencies was investigated by numerical simulation.The linear response of neuron membrane potential to the lowfrequency signal can achieve optimal by modulating the amplitude of highfrequency signal to an appropriate value, where the phenomenon of vibrational resonance occurs.It is shown that the highfrequency signal can help the weak lowfrequency signal detection and information propagation.Furthermore, the influences of parameters of the map and input signals on the resonance dynamics were also studied.