Dynamics of Pulse-Coupled Integrate-and-Fire Oscillators

Synchronization and phase-locking are commonly observed phenomena that occur in biological and physical oscillators under specific conditions. Mirollo and Strogatz modeled the pulse-coupled integrate-and-fire oscillators which are characterized by a state variable and a phase variable. These two variables are related by a concave down action potential function. As an oscillator reaches its maximum state, it fires. The firing reset the state and phase of the oscillator back to 0 and push other oscillators up (in vertical direction) by in the state-phase plane. Our research extended on Mirollo and Strogatz\u27 work in two directions. First, we assign different coupling strengths to different oscillators. Second, we attach different oscillators to different action potential functions. We present how variations in the relative magnitudes of the coupling strength(s) and initial states of the oscillators eventually determine the dynamics of these oscillators