Circuit Implementation and Dynamics of a Two-Dimensional MOSFET Neuron Model

We propose a two-dimensional neuron model using metal-oxide-semiconductor field-effect-transistors (MOSFETs). It can be implemented with a compact circuitry. This is because we designed its phase portrait structure utilizing the curves native to the MOSFET circuitries. Bifurcation theory is applied to tune the characteristics of the circuitry. Biological neurons can be divided into two main classes based on their responses to sustained current stimuli: classes I and II. At the onset of firing, the firing frequency of class I neurons is asymptotically zero, while that of class II neurons is nonzero. It is generally accepted that classes I and II excitabilities are produced by a saddle-node bifurcation and a subcritical Hopf bifurcation, respectively. Class I* neurons, which belong to a subclass of class I, are characterized by a phase plane structure called a narrow channel. By changing a few circuit parameters, our circuitry can achieve class I without a narrow channel, class I*, and class II. The proposed circuitry is compatible with standard complementary metal-oxide-semiconductor (CMOS) processes. Hence, it can be easily implemented in an analog very-large-scale integrated (VLSI) circuit; further, large networks can be constructed by using this circuitry. We implemented and tested our circuitry, that was constructed using discrete components. We analyzed the responses to singlet, doublet, periodic pulses, and sustained current stimuli; further, we demonstrated that our circuitry inherited three critical properties of biological neurons: (a) the fundamental abilities of excitable cells, (b) neural excitability such as of classes I and II, and (c) an ability to generate chaotic responses to periodic pulse stimuli. We then applied the bifurcation theory to our circuitry and verified its mathematical structure using XPPAUT software. Furthermore, the simulation results on a gap junction (GJ)-coupled network comprising class I* neurons revealed the genesis of itinerant dynamics similar to that found by Fujii et al..

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