Authors: Yan Dong Chu, Jian Gang Zhang, Xian Feng Li, Ying Xiang Chang

Abstract: In this paper, the dynamical behaviors of the centrifugal flywheel governor with external
disturbance are discussed, and the system exhibits exceedingly complicated dynamic behaviors. The
influence of system parameter on the chaotic system is discussed through Lyapunov-exponents
spectrum and global bifurcation diagram, which accurately portray the partial dynamic behavior of
the system. It is chaotic with proper system parameter, and we utilize Poincaré sections to study the
Hopf bifurcation and chaos forming of the centrifugal flywheel governor system. Then, we utilize
coupled-feedback control and adaptive control to realize the chaotic synchronization and obtain the
conditions of chaos synchronization. Finally, we carry on the theory proof using the Lyapunov
stability theory to the obtained conditions, the theoretical proof and number simulation shows the
effectiveness of these methods.

309

Authors: You Jie Ma, Xiao Shuang Li, Xue Song Zhou, Ji Li, Hu Long Wen, Li Ying Jia

Abstract: In power system, when the overload of large-scale power grid results in serious disaster, the nonlinear dynamic bifurcation is obvious. It will be effective to delay the occurrence of bifurcation through the bifurcation control method, so workers have enough time to take protective measures. We can also design an appropriate controller to prevent these kinds of dangerous disaster effectively. This paper outlines a number of common bifurcation control method, and use one of these method to design a bifurcation controller so as to control the hopf bifurcation in power system and make a Simulation on it.

84

Authors: Ze Jin Shang, Zhong Min Wang

Abstract: The recovery force of shape memory alloy spring is described by using polynomial constitutive equation. The nonlinear dynamic model of forced vibration for the shape memory alloy spring oscillator is derived. Numerical simulations are performed by a fourth-order Runge-Kutta method. The bifurcation diagram and Lyapunov-exponent spectrum are presented while the dimensionless temperature, the dimensionless damping coefficient or the dimensionless amplitude of exciting force is varied respectively, thus the bifurcation of the system is investigated. Furthermore, the periodic and chaotic motions of the system are analyzed by means of the displacement time history diagram, the phase portrait, the Poincare section diagram and the power spectrum with different parameters. The results show that the periodic or chaotic motion of the system occur by changing temperature, damping coefficient and amplitude of exciting force, thus the vibration of the system could be controlled.

3958

Authors: Bai Zhan Shi, Xiang Feng Gou, Quan Lei Chen

Abstract: A third-order circuit system with nonlinear negative capacitance is studied. The dynamical equation and state equation of the system are established. By the phase portraits, the motions of the system are studied under the definite parameters. And by bifurcation diagram, the route from periodic motion to chaos is studied under the presented system parameters. Two controllers are constructed to control the chaos of a third-order circuit system with nonlinear negative capacitance. One controller is nonlinear and the other is linear. The phase plane portraits and bifurcation diagram of the controlled system are obtained. The effect of the nonlinear controller is better than the linear one. The threshold values of the control values of the two control method are obtained. The advantages of the two controlled methods are that the collect of the control signals are simple and can put on any time and the chaotic system can be asymptotically stabilized to equilibriums with small control. The orbits of the system can be controlled by these two methods according to our target.

2263

Authors: Zhen Wang, Wei Sun, Zhou Chao Wei

Abstract: The dynamics of a non-autonomous chaotic system with one cubic nonlinearity is studied through numerical and experimental investigations in this paper. A method for calculating Lyapunov exponents (LEs), Lyapunov dimension (LD) from time series is presented. Furthermore, some complex dynamic behaviors such as periodic, quasi-periodic motion and chaos which occurred in the system are analyzed, and a route to chaos, phase portraits, Poincare sections, bifurcation diagrams are observed. Finally, a first order differential controller for the non-autonomous system is designed. Also some dynamics such as Poincare sections, bifurcation diagrams for specific control parameter values of the controlled system are showed using numerical and experimental simulations.

204