An efficient analysis of FitzHugh-Nagumo circuit model

FitzHugh-Nagumo, FHN, is a most critically significant Neural Cell method which is effectively capable of modeling the synaptic behavior by leveraging van-der-pol oscillators. The FitzHugh-Nagumo model makes use of common circuitry of FHNs, remarkably similar to the very conventional LC oscillators. Conventional LC oscillators, needless to say, have been largely deployed and comprehensively studied for quite some time. Notwithstanding its similarity to other LC oscillators, FitzHugh-Nagumo contains a resistor in series with the circuit that makes it inconsistent with other LC oscillator models. In this paper, a productive circuit technique is used to make FitzHugh-Nagumo circuit analogous to a LC conventional oscillator, which consequently provides the capability of using analytical approaches on these systems. This gives the designer of neural cells the opportunity of taking advantage of the vast knowledge about oscillatory systems. The proposed circuit model has been verified in terms of accuracy and compatibility for free-running, locked, and unlocked states. In addition, a theoretical analysis, aiming to clarify the background principle of the FitzHugh-Nagumo design process, is also provided. The simulation results which are performed using TSMC 180 nm CMOS technology represent a good agreement between theory and simulation.