Vibrational resonance in the FitzHugh–Nagumo neuron model under state-dependent time delay

We propose a nonlinear FitzHugh-Nagumo neuronal model with an asymmetric potential driven by both a high-frequency signal and a low-frequency signal. Our numerical analysis focuses on the influence of a state-dependent time delay on vibrational resonance and delay-induced resonance phenomena. The response amplitude at the low-frequency signal is explored to characterize the vibrational resonance and delay-induced resonance. Our results show that for smaller values of the amplitude of the state-dependent time-delay velocity component, vibrational resonance and multi-resonance occur in the neuronal model. For large values of the high-frequency excitation amplitude, vibrational resonance appears with one peak. Furthermore, we observe a change in the response when the amplitude of the state-dependent time-delay velocity component increases. In addition, we analyze how the state-dependent time-delay position and velocity components can give birth to delay-induced resonance for separate and together. The key findings of this work demonstrate that the state-dependent time-delay velocity component plays a crucial role in both phenomena. Specifically, the delay parameter serves as a critical control factor, capable of triggering the onset of the two resonances.