Pulse-coupled resonate-and-fire models

Numerical simulations and theory are used to discuss the antiphase state of a system in which two resonate-and-fire models are pulse coupled. First, numerical simulations show that antiphase states are an attractor of this model. Next, the stability of the antiphase states is explained theoretically by constructing a return map of the firing times. The condition for which the stability changes is an extremely simple equation. The authors created a phase diagram based on the theory and discovered that there are two types of antiphase states. One of these is unique to the resonate-and-fire model and does not appear in the integrate-and-fire model. Finally, the authors execute numerical simulations to verify the correctness of the theory of stability.