Synchronization of Bursting Pulse-Coupled Neurons in a Simulation Modeling Environment

Bursting is a special dynamic mode of neurons that consists of several consecutive spikes separated by a period of quiescence. This paper considers the synchronization of two non-identical neurons capable of both spiking and bursting behavior connected by a unidirectional pulse coupling. Unlike most studies, which focus on purely mathematical modeling and numerical simulations, we use simulation modeling of a neuron based on a phase-locked loop (PLL) in addition to the conventional solving of ODEs. Using these two approaches, we demonstrate the fundamental possibility of synchronizing two neurons operating in different dynamic modes. Synchronization regions are constructed in the system parameter space. It is shown that synchronization is achieved both for two spiking neurons and for neurons generating bursting activity. The results obtained are of interest from either a fundamental perspective, as an example of a complex nonlinear system with rich dynamic behavior, or from an applied perspective. In particular, the proposed model can be used in the field of neuromorphic electronics, where not only biological plausibility is important but also the possibility of simple hardware implementation. Differences between the simulation model and the results of numerical solution of ODEs are also demonstrated, revealing the importance of proper simulation frameworks at different design levels of neuromorphic electronics.