By introducing the periodic parameter-switching signal to the Lorenz oscillator, a switched dynamic model is established. In order to investigate the mechanism of the behaviors of the whole system, bifurcation sets of...By introducing the periodic parameter-switching signal to the Lorenz oscillator, a switched dynamic model is established. In order to investigate the mechanism of the behaviors of the whole system, bifurcation sets of the subsystems are derived and the Poincar6 map of the switched system is defined by suitable local sections and local maps. Under certain parameter conditions, symmetric periodic oscillations may be observed. With the variation of parameter, the symmetry-breaking bifurcation mecha- nisms of the symmetric periodic oscillations can be understood by calculating the associated maximal Lyapunov exponent and Floquet multiplies. Meanwhile, the parameter values of the related local bifurcations, such as saddle-node, pitchfork and peri- od-doubling bifurcations are calculated based on the Floquet multiplies.展开更多
This paper considers the synchronization of two coupled Hindmarsh-Rose neurons by a pacemaker.Based on the stability theory of differential equations,the complete synchronization of this pacemaker neuron model is reac...This paper considers the synchronization of two coupled Hindmarsh-Rose neurons by a pacemaker.Based on the stability theory of differential equations,the complete synchronization of this pacemaker neuron model is reached.Moreover,we also show that pacemaker can enhance or induce synchronization.Numerical simulations are given to illustrate the main results.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 21276115, 11272135, 11202085)the Scientific Research Innovation Foundation of Jiangsu Province (Grant No. CXZZ13-0653)the Natural Science Foundation for Colleges and Universities of Jiangsu Province (Grant No. 11KJB130001)
文摘By introducing the periodic parameter-switching signal to the Lorenz oscillator, a switched dynamic model is established. In order to investigate the mechanism of the behaviors of the whole system, bifurcation sets of the subsystems are derived and the Poincar6 map of the switched system is defined by suitable local sections and local maps. Under certain parameter conditions, symmetric periodic oscillations may be observed. With the variation of parameter, the symmetry-breaking bifurcation mecha- nisms of the symmetric periodic oscillations can be understood by calculating the associated maximal Lyapunov exponent and Floquet multiplies. Meanwhile, the parameter values of the related local bifurcations, such as saddle-node, pitchfork and peri- od-doubling bifurcations are calculated based on the Floquet multiplies.
基金supported by the National Natural Science Foundation of China (1087201410802012)
文摘This paper considers the synchronization of two coupled Hindmarsh-Rose neurons by a pacemaker.Based on the stability theory of differential equations,the complete synchronization of this pacemaker neuron model is reached.Moreover,we also show that pacemaker can enhance or induce synchronization.Numerical simulations are given to illustrate the main results.
