Autonomous integrate-and-fire model with vibration

We propose an integrate-and-fire model with 2D integration and instantaneous firing. This system exhibits period doubling bifurcation to chaos, periodic windows, tangent bifurcation and so on. Connecting two pieces of the model by switching pulses, we construct a mutually coupled system. It exhibits chaos synchronization, periodic synchronization and related bifurcation. These phenomena are analyzed using a mapping procedure and verified in the laboratory.