Model for Coupling Scheme and its Impact on Neurons Behaviour

Abstract

Collective oscillations is typical phenomena observed in the systems biology including neurons. Investigating the mechanisms for which it occurs in neural networks evokes a significant interest among neuroscientists. From mathematical point of view, the coupling schemes rule the neuron’s behaviours ranging from microscopic to macroscopic scales. This paper aims to study the impacts of coupling schemes in a minimal network of two fully coupled identical oscillators (e.g., neurons). We proceed with the research by employing the numerical approach and time-series analysis. We consider both Kuramoto-like oscillator and Leaky integrate-and-fire neuron as the objects of study. In the former case, we found the phase of two oscillators are perfectly locked and stable if their frequency are identical, as stated by the main theorem. In the latter case, the membrane potentials of two neurons are perfectly synchronized, characterized by the same firing rate, due to the effect of excitatory delta pulses.