State Key Lab of Mechanics and Control for Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People's Republic of China.
School of Mechanical and Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, People's Republic of China.
Comput Biol Med. 2014 Feb;45:80-6. doi: 10.1016/j.compbiomed.2013.11.022. Epub 2013 Dec 4.
In the present paper, the phenomenon of vibrational resonance in a time-varying delayed FitzHugh-Nagumo system that is driven by two-frequency periodic signals is reported. Via a numerical simulation, the periodic vibrational resonances are found to be induced by the time-varying delay feedback under the condition that the delayed feedback strength is small, and then along with the increase of the delayed feedback strength K within the slow period (i.e., the period of low-frequency signal), the single resonance turns into multiple resonances. However, if the delayed feedback strength K is big enough, the resonance no longer occurs. More interestingly, the multiple resonances can also turn into a single resonance in a cycle by modulating the amplitude F of high-frequency signal. Furthermore, both the resonance region and the resonance amplitude are found to be able to be controlled by the time-varying delay. Finally, it is found that the regular motion of the system can be enhanced by the time-varying delay feedback and then more regular motion will present if the resonance does not occur.
本文报道了在双频周期信号驱动下，时变时滞 FitzHugh-Nagumo 系统中振动共振的现象。通过数值模拟发现，在延迟反馈强度较小的情况下，时变延迟反馈会诱发周期性振动共振，随着慢周期（即低频信号的周期）内延迟反馈强度 K 的增加，单共振变为多共振。然而，如果延迟反馈强度 K 足够大，共振就不再发生。更有趣的是，通过调制高频信号的幅度 F，多个共振也可以在一个周期内转变为单个共振。此外，共振区域和共振幅度都可以通过时变延迟来控制。最后发现，时变延迟反馈可以增强系统的规则运动，如果不发生共振，系统将呈现出更加规则的运动。
