In this paper, the synchronization of the fractional-order generalized augmented Lti system is investigated. Based on the predictor--corrector method, we obtain phase portraits, bifurcation diagrams, Lyapunov exponent...In this paper, the synchronization of the fractional-order generalized augmented Lti system is investigated. Based on the predictor--corrector method, we obtain phase portraits, bifurcation diagrams, Lyapunov exponent spectra, and Poincar6 maps of the fractional-order system and find that a four-wing chaotic attractor exists in the system when the system pa- rameters change within certain ranges. Further, by varying the system parameters, rich dynamical behaviors occur in the 2.7-order system. According to the stability theory of a fractional-order linear system, and adopting the linearization by feedback method, we have designed a nonlinear feedback controller in our theoretical analysis to implement the synchro- nization of the drive system with the response system. In addition, the synchronization is also shown by an electronic circuit implementation for the 2.7-order system. The obtained experiment results accord with the theoretical analyses, which further demonstrate the feasibility and effectiveness of the proposed synchronization scheme.展开更多
Over the past decades, complex networks have been prosperous greatly in various fields of sciences and engineering. Much attention has been given to investigate the synchronization of complex networks in recent years....Over the past decades, complex networks have been prosperous greatly in various fields of sciences and engineering. Much attention has been given to investigate the synchronization of complex networks in recent years. However, few work has done for the networks with uncertain parameters and unknown topology. In this paper, to further reveal the dynamical mechanism in complex networks with time delays, an uncertain general complex dynamical network with delayed nodes is studied. By constructing a drive network and a suitable slave network, several novel criteria for the networks consisting of the identical nodes and different nodes have been obtained based on the adaptive feedback method. Particularly, the hypotheses and the proposed adaptive laws for network synchronization are simple and can be readily applied in practical applications. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed synchronization criteria.展开更多
A novel hyperchaotic system derived from Liu system is proposed in this paper. Lyapunov exponent, phase portrait and Poincare mapping are given to verify that the system is hyperchaotic. A controller is designed to co...A novel hyperchaotic system derived from Liu system is proposed in this paper. Lyapunov exponent, phase portrait and Poincare mapping are given to verify that the system is hyperchaotic. A controller is designed to compel the hyperchaotic system to converge into the equilibrium. It is proved theoretically that this control law is feasible and valid by Lyapunov second method. Based on linear feedback synchronization control principle, synchronization control of the novel hyperchaotic system is realized. Numerical simulation shows that this synchronization method is simple and effective. As long as the proper linear feedback control vector is chosen, it is easy to achieve the rapid synchronization between the driving system and response system.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.61174094)the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.11202148)
文摘In this paper, the synchronization of the fractional-order generalized augmented Lti system is investigated. Based on the predictor--corrector method, we obtain phase portraits, bifurcation diagrams, Lyapunov exponent spectra, and Poincar6 maps of the fractional-order system and find that a four-wing chaotic attractor exists in the system when the system pa- rameters change within certain ranges. Further, by varying the system parameters, rich dynamical behaviors occur in the 2.7-order system. According to the stability theory of a fractional-order linear system, and adopting the linearization by feedback method, we have designed a nonlinear feedback controller in our theoretical analysis to implement the synchro- nization of the drive system with the response system. In addition, the synchronization is also shown by an electronic circuit implementation for the 2.7-order system. The obtained experiment results accord with the theoretical analyses, which further demonstrate the feasibility and effectiveness of the proposed synchronization scheme.
基金This work was jointly supported by the National Natural Science Foundation of China under Grant No. 11047114, the Key Project of Chinese Ministry of Education under Grant No. 210141, and the Youth Project of Hubei Education Department under Grant No. Q20101609.
文摘Over the past decades, complex networks have been prosperous greatly in various fields of sciences and engineering. Much attention has been given to investigate the synchronization of complex networks in recent years. However, few work has done for the networks with uncertain parameters and unknown topology. In this paper, to further reveal the dynamical mechanism in complex networks with time delays, an uncertain general complex dynamical network with delayed nodes is studied. By constructing a drive network and a suitable slave network, several novel criteria for the networks consisting of the identical nodes and different nodes have been obtained based on the adaptive feedback method. Particularly, the hypotheses and the proposed adaptive laws for network synchronization are simple and can be readily applied in practical applications. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed synchronization criteria.
文摘A novel hyperchaotic system derived from Liu system is proposed in this paper. Lyapunov exponent, phase portrait and Poincare mapping are given to verify that the system is hyperchaotic. A controller is designed to compel the hyperchaotic system to converge into the equilibrium. It is proved theoretically that this control law is feasible and valid by Lyapunov second method. Based on linear feedback synchronization control principle, synchronization control of the novel hyperchaotic system is realized. Numerical simulation shows that this synchronization method is simple and effective. As long as the proper linear feedback control vector is chosen, it is easy to achieve the rapid synchronization between the driving system and response system.
