Based on the chaotic geomagnetic field model, a non-smooth factor is introduced to explore complex dynamical behaviors of a system with multiple time scales. By regarding the whole excitation term as a parameter, bifu...Based on the chaotic geomagnetic field model, a non-smooth factor is introduced to explore complex dynamical behaviors of a system with multiple time scales. By regarding the whole excitation term as a parameter, bifurcation sets are derived, which divide the generalized parameter space into several regions corresponding to different kinds of dynamic behaviors. Due to the existence of non-smooth factors, different types of bifurcations are presented in spiking states, such as grazing-sliding bifurcation and across-sliding bifurcation. In addition, the non-smooth fold bifurcation may lead to the appearance of a special quiescent state in the interface as well as a non-smooth homoclinic bifurcation phenomenon. Due to these bifurcation behaviors, a special transition between spiking and quiescent state can also occur.展开更多
A modified slow-fast analysis method is presented for the periodically excited non-autonomous dynamical system with an order gap between the exciting frequency and the natural frequency.By regarding the exciting term ...A modified slow-fast analysis method is presented for the periodically excited non-autonomous dynamical system with an order gap between the exciting frequency and the natural frequency.By regarding the exciting term as a slow-varying parameter,a generalized autonomous fast subsystem can be defined,the equilibrium branches as well as the bifurcations of which can be employed to account for the mechanism of the bursting oscillations by combining the transformed phase portrait introduced.As an example,a typical periodically excited Hartley model is used to demonstrate the validness of the method,in which the exciting frequency is far less than the natural frequency.The equilibrium branches and their bifurcations of the fast subsystem with the variation of the slow-varying parameter are presented.Bursting oscillations for two typical cases are considered,which reveals that,fold bifurcation may cause the the trajectory to jump between different equilibrium branches,while Hopf bifurcation may cause the trajectory to oscillate around the stable limit cycle.展开更多
This paper proposes a two-to-one internal resonance to widen the bandwidth of vibratory energy harvesters.To describe the improved characteristic,an electromagnetic spring-pendulum harvester is designed.Approximate an...This paper proposes a two-to-one internal resonance to widen the bandwidth of vibratory energy harvesters.To describe the improved characteristic,an electromagnetic spring-pendulum harvester is designed.Approximate analytical solutions of the electromechanical coupled system are carried out by introducing the method of multiple scales,and the frequency response relationships of the displacement and the current are obtained.The character of broadband harvesting performance is examined,the two peaks and double jump phenomena for variation of design parameters were observed.The effect of key control parameters on the harvesters bandwidth is considered,and the nonlinear behaviors of the harvester are validated via numerical results.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11472116)the Key Program of the National Natural Science Foundation of China(Grant No.11632008)the Postgraduate Research&Practice Innovation Program of Jiangsu Province,China(Grant No.KYCX17 1784)
文摘Based on the chaotic geomagnetic field model, a non-smooth factor is introduced to explore complex dynamical behaviors of a system with multiple time scales. By regarding the whole excitation term as a parameter, bifurcation sets are derived, which divide the generalized parameter space into several regions corresponding to different kinds of dynamic behaviors. Due to the existence of non-smooth factors, different types of bifurcations are presented in spiking states, such as grazing-sliding bifurcation and across-sliding bifurcation. In addition, the non-smooth fold bifurcation may lead to the appearance of a special quiescent state in the interface as well as a non-smooth homoclinic bifurcation phenomenon. Due to these bifurcation behaviors, a special transition between spiking and quiescent state can also occur.
基金supported by the National Natural Science Foundation of China(Grants11632008 and 11872189)
文摘A modified slow-fast analysis method is presented for the periodically excited non-autonomous dynamical system with an order gap between the exciting frequency and the natural frequency.By regarding the exciting term as a slow-varying parameter,a generalized autonomous fast subsystem can be defined,the equilibrium branches as well as the bifurcations of which can be employed to account for the mechanism of the bursting oscillations by combining the transformed phase portrait introduced.As an example,a typical periodically excited Hartley model is used to demonstrate the validness of the method,in which the exciting frequency is far less than the natural frequency.The equilibrium branches and their bifurcations of the fast subsystem with the variation of the slow-varying parameter are presented.Bursting oscillations for two typical cases are considered,which reveals that,fold bifurcation may cause the the trajectory to jump between different equilibrium branches,while Hopf bifurcation may cause the trajectory to oscillate around the stable limit cycle.
基金supported by the National Natural Science Foundation of China(Grants 11632008,11702119,and 11972173)the Natural Science Foundation of Jiangsu Province(Grant BK20170565)+1 种基金the Qing Lan Project of Jiangsu Provincethe Training program for Young Talents of Jiangsu University.
文摘This paper proposes a two-to-one internal resonance to widen the bandwidth of vibratory energy harvesters.To describe the improved characteristic,an electromagnetic spring-pendulum harvester is designed.Approximate analytical solutions of the electromechanical coupled system are carried out by introducing the method of multiple scales,and the frequency response relationships of the displacement and the current are obtained.The character of broadband harvesting performance is examined,the two peaks and double jump phenomena for variation of design parameters were observed.The effect of key control parameters on the harvesters bandwidth is considered,and the nonlinear behaviors of the harvester are validated via numerical results.
