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
Rotor systems supported by angular contact ball bearings are complicated due to nonlinear Hertzian contact force. In this paper, nonlinear bearing forces of ball bearing under five-dimensional loads are given, and 5-D...Rotor systems supported by angular contact ball bearings are complicated due to nonlinear Hertzian contact force. In this paper, nonlinear bearing forces of ball bearing under five-dimensional loads are given, and 5-DOF dynamic equations of a rigid rotor ball bearing system are established. Continuation-shooting algorithm for periodic solutions of the nonlinear non-autonomous dynamic system and Floquet multipliers of the system are used. Furthermore, the bifurcation and stability of the periodic motion of the system in different parametric domains are also studied. Results show that the bifurcation and stability of period-1 motion vary with structural parameters and operating parameters of the rigid rotor ball bearing system. Avoidance of unbalanced force and bending moment, appropriate initial contact angle, axial load and damping factor help enhance the unstable rotating speed of period-1 motion.展开更多
By means of the theory on the semi-global C^1 solution to the mixed initialboundary value problem （IBVP） for first order quasilinear hyperbolic systems, we establish the exact controllability for general nonautonomo...By means of the theory on the semi-global C^1 solution to the mixed initialboundary value problem （IBVP） for first order quasilinear hyperbolic systems, we establish the exact controllability for general nonautonomous first order quasilinear hyperbolic systems with general nonlinear boundary conditions.展开更多
The auto-correlation function and the cross-correlation of an autonomous stochastic system with nonlinear time-delayed feedback are investigated by using the stochastic simulation method. There are prominent differenc...The auto-correlation function and the cross-correlation of an autonomous stochastic system with nonlinear time-delayed feedback are investigated by using the stochastic simulation method. There are prominent differences be- tween the roles of quadratic time-delayed feedback and cubic time-delayed feedback on the correlations of an autonomous stochastic system. Under quadratic time-delayed feedback, the nonlinear time delay fails to improve the noisy state of the autonomous stochastic system, the auto-correlation decreases monotonously to zero, and the cross-correlation increases monotonously to zero with the decay time. Under cubic time-delayed feedback, the nonlinear time delay can improve the noisy state of the autonomous stochastic system; the auto-correlation and the cross-correlation show periodical oscillation and attenuation, finally tending to zero with the decay time. Comparing the correlations of the system between with nonfinear time-delayed feedback and linear time-delayed feedback, we find that nonlinear time-delayed feedback lowers the correlation strength of the autonomous stochastic system.展开更多
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.
基金Supported by National Natural Science Foundation of China (No.50905061)the Fundamental Research Funds for Central Universities
文摘Rotor systems supported by angular contact ball bearings are complicated due to nonlinear Hertzian contact force. In this paper, nonlinear bearing forces of ball bearing under five-dimensional loads are given, and 5-DOF dynamic equations of a rigid rotor ball bearing system are established. Continuation-shooting algorithm for periodic solutions of the nonlinear non-autonomous dynamic system and Floquet multipliers of the system are used. Furthermore, the bifurcation and stability of the periodic motion of the system in different parametric domains are also studied. Results show that the bifurcation and stability of period-1 motion vary with structural parameters and operating parameters of the rigid rotor ball bearing system. Avoidance of unbalanced force and bending moment, appropriate initial contact angle, axial load and damping factor help enhance the unstable rotating speed of period-1 motion.
基金Project supported by Specialized Research Fund for the Doctoral Program of Higher Education.
文摘By means of the theory on the semi-global C^1 solution to the mixed initialboundary value problem （IBVP） for first order quasilinear hyperbolic systems, we establish the exact controllability for general nonautonomous first order quasilinear hyperbolic systems with general nonlinear boundary conditions.
基金Supported by the National Natural Science Foundation of China under Grant No.11265012Yunnan Province Open Key Laboratory of Mechanics in Colleges and Universities
文摘The auto-correlation function and the cross-correlation of an autonomous stochastic system with nonlinear time-delayed feedback are investigated by using the stochastic simulation method. There are prominent differences be- tween the roles of quadratic time-delayed feedback and cubic time-delayed feedback on the correlations of an autonomous stochastic system. Under quadratic time-delayed feedback, the nonlinear time delay fails to improve the noisy state of the autonomous stochastic system, the auto-correlation decreases monotonously to zero, and the cross-correlation increases monotonously to zero with the decay time. Under cubic time-delayed feedback, the nonlinear time delay can improve the noisy state of the autonomous stochastic system; the auto-correlation and the cross-correlation show periodical oscillation and attenuation, finally tending to zero with the decay time. Comparing the correlations of the system between with nonfinear time-delayed feedback and linear time-delayed feedback, we find that nonlinear time-delayed feedback lowers the correlation strength of the autonomous stochastic system.
