Siewe Siewe, M., Rajasekar, S., Coccolo, M., & Sanjuán, M. A. F. (2024). Vibrational resonance in the FitzHugh-Nagumo neuron model under state-dependent time delay. arXiv preprint arXiv:2410.06861v1.
This research paper investigates the influence of state-dependent time delay, particularly the velocity component, on the occurrence and behavior of vibrational resonance and delay-induced resonance in a FitzHugh-Nagumo neuron model.
The authors employ numerical analysis to study a modified FitzHugh-Nagumo neuron model incorporating an asymmetric double-well potential, state-dependent time delay (modeled using a sigmoid function), and a biharmonic force. They analyze the system's response amplitude at the low frequency to characterize vibrational resonance and delay-induced resonance under varying parameters of the time delay and forcing frequencies.
The study demonstrates that the state-dependent time delay, specifically the velocity component, plays a crucial role in regulating the emergence and characteristics of both vibrational resonance and delay-induced resonance in the FitzHugh-Nagumo neuron model. This finding suggests potential avenues for controlling these resonance phenomena by manipulating the time delay parameters.
This research enhances our understanding of how time delays, particularly state-dependent ones, influence the dynamics of neuronal systems. The findings have implications for comprehending information processing in neurons and potentially for developing treatments for neurological disorders characterized by abnormal neuronal firing patterns.
The study primarily relies on numerical analysis of a specific neuron model. Further research could explore the generalizability of these findings to other neuron models and experimental validation in biological systems. Additionally, investigating the impact of noise and network interactions on these resonance phenomena in the presence of state-dependent time delays would be valuable.
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