The study of controlling high-current proton beam halo-chaos has become a key concerned issue for manyimportant applications. In this paper, time-delayed feedback control method is proposed for beam halo-chaos. Partic...The study of controlling high-current proton beam halo-chaos has become a key concerned issue for manyimportant applications. In this paper, time-delayed feedback control method is proposed for beam halo-chaos. Particle incell simulation results show that the method is very effective and has some advantages for high-current beam experimentsand engineering.展开更多
In this paper, inertia is added to a simplified neuron system with time delay. The stability of the trivial equilibrium of the net- work is analyzed and the condition for the existence of Hopf bifurcation is obtained ...In this paper, inertia is added to a simplified neuron system with time delay. The stability of the trivial equilibrium of the net- work is analyzed and the condition for the existence of Hopf bifurcation is obtained by discussing the associated characteristic equation. Hopf bifurcation is investigated by using the perturbation scheme without the norm form theory and the center man- ifold theorem. Numerical simulations are performed to validate the theoretical results and chaotic behaviors are observed. Phase plots, time history plots, power spectra, and Poincar6 section are presented to confirm the chaoticity. To the best of our knowledge, the chaotic behavior in this paper is new to the previously published works.展开更多
While the significance of oscillator dynamics and coupling structure to synchronization behaviors has been well addressed in the literature, little attention has been paid to the possible influence of coupling functio...While the significance of oscillator dynamics and coupling structure to synchronization behaviors has been well addressed in the literature, little attention has been paid to the possible influence of coupling functions. In the present paper, adopting the scheme of dual-channel time-delayed couplings, we investigate how the synchronization behaviors of networked chaotic oscillators are influenced by parameters in the coupling functions. It is found that, with the introduction of the second coupling channel, the synchronization region, as calculated according to the method of master stability function(MSF), can be largely modified. In particular, by a slight change of the time delay, it is found that the synchronization region can be significantly adjusted, or even switched from non-existing to existing. We demonstrate this interesting phenomenon for both situations of processing and propagation induced time delays, as well as for different coupling functions. Our studies shed new light on the mechanism of chaos synchronization, and may potentially be used for the control of complex network dynamics.展开更多
In this paper, we propose a method for the projective synchronization between two different chaotic systems with variable time delays. Using active control approach, the suitable controller is constructed to make the ...In this paper, we propose a method for the projective synchronization between two different chaotic systems with variable time delays. Using active control approach, the suitable controller is constructed to make the states of two different diverse time delayed systems asymptotically synchronize up to the desired scaling factor. Based on the Lyapunov stability theory, the sufficient condition for the projective synchronization is calculated theoretically. Numerical simulations of the projective synchronization between Maekey-Glass system and Ikeda system with variable time delays are shown to validate the effectiveness of the proposed algorithm.展开更多
基金The project supported by National Natural Science Foundation of China under Grant Nos.10247005,70071047,and 19875080
文摘The study of controlling high-current proton beam halo-chaos has become a key concerned issue for manyimportant applications. In this paper, time-delayed feedback control method is proposed for beam halo-chaos. Particle incell simulation results show that the method is very effective and has some advantages for high-current beam experimentsand engineering.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11202068 and 11032009)
文摘In this paper, inertia is added to a simplified neuron system with time delay. The stability of the trivial equilibrium of the net- work is analyzed and the condition for the existence of Hopf bifurcation is obtained by discussing the associated characteristic equation. Hopf bifurcation is investigated by using the perturbation scheme without the norm form theory and the center man- ifold theorem. Numerical simulations are performed to validate the theoretical results and chaotic behaviors are observed. Phase plots, time history plots, power spectra, and Poincar6 section are presented to confirm the chaoticity. To the best of our knowledge, the chaotic behavior in this paper is new to the previously published works.
基金supported by the National Natural Science Foundation of China(Grant No.40976114)the Fundamental Research Funds for the Central Universities(Grant No.GK201303002)
文摘While the significance of oscillator dynamics and coupling structure to synchronization behaviors has been well addressed in the literature, little attention has been paid to the possible influence of coupling functions. In the present paper, adopting the scheme of dual-channel time-delayed couplings, we investigate how the synchronization behaviors of networked chaotic oscillators are influenced by parameters in the coupling functions. It is found that, with the introduction of the second coupling channel, the synchronization region, as calculated according to the method of master stability function(MSF), can be largely modified. In particular, by a slight change of the time delay, it is found that the synchronization region can be significantly adjusted, or even switched from non-existing to existing. We demonstrate this interesting phenomenon for both situations of processing and propagation induced time delays, as well as for different coupling functions. Our studies shed new light on the mechanism of chaos synchronization, and may potentially be used for the control of complex network dynamics.
基金Supported by Research Project of Hubei Provincial Department of Education under Grant No. Q20101609Foundation of Wuhan Textile University under Grant No. 105040
文摘In this paper, we propose a method for the projective synchronization between two different chaotic systems with variable time delays. Using active control approach, the suitable controller is constructed to make the states of two different diverse time delayed systems asymptotically synchronize up to the desired scaling factor. Based on the Lyapunov stability theory, the sufficient condition for the projective synchronization is calculated theoretically. Numerical simulations of the projective synchronization between Maekey-Glass system and Ikeda system with variable time delays are shown to validate the effectiveness of the proposed algorithm.
