Vibrational resonance in the FitzHugh–Nagumo system with time-varying delay feedback

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.