Electronic Bursting Neuron: design, equations and hardware implementation

Electronic neurons are a keystone for construction of the spiking neural networks which have numerous applications in neuroprosthetics, artificial memory, intensive calculations etc. A number of concepts of electronic neurons has been already proposedm with some of them implemented in hardware. However, new schemes are of significant interest since the existing ones do not fit all requirements: either they are too complex and expensive in realization, or they are not able to demonstrate all demanded regimes, or their do not have a appropriate mathematical description and therefore may be investigated only experimentally etc.
In this study we propose a new design of bursting electronic neuron constructed as a circuit implementation of the equations of a phase-locked loop system. To succeed, we use a novel hybrid approach: we start from the phenomenological equations providing the demanded, then we adjust and modify these equations to simplify the implementation rather than implementing the biophysical equations into thee hardware directly or writing equations for the already constructed circuit. The resulting circuit is simple in implementation and well matches the underlying equations. It can be used for description of not only a single neuron, but small neural circuits too.