Synchronicity of Biological Oscillators

The integrate-and-fire model is an oft-used model to describe biological oscillators. In their seminal work, Mirollo and Strogatz discovered important conditions that guarantee synchronization between N-oscillators. This paper explores a wider variety of conditions that determine synchronicity. We examine different types of action potential curves and we break from conventional assumptions of identical oscillators. We prove various conditions for which synchrony will or will not occur