Globally Coupled Resonate-and-Fire Models

Pulse-coupled resonate-and-fire models.

We analyze two pulse-coupled resonate-and-fire neurons. Numerical simulation reveals that an antiphase state is an attractor of this model. We can analytically explain the stability of antiphase states by means of a return map of firing times, which we propose in this paper. The resultant stability condition turns out to be quite simple. The phase diagram based on our theory shows that there ar...

Resonate-and-fire neurons

We suggest a simple spiking model-resonate-and-fire neuron, which is similar to the integrate-and-fire neuron except that the state variable is complex. The model provides geometric illustrations to many interesting phenomena occurring in biological neurons having subthreshold damped oscillations of membrane potential. For example, such neurons prefer a certain resonant frequency of the input t...

First passage time densities in resonate-and-fire models.

Motivated by the dynamics of resonant neurons we discuss the properties of the first passage time (FPT) densities for non-Markovian differentiable random processes. We start from an exact expression for the FPT density in terms of an infinite series of integrals over joint densities of level crossings, and consider different approximations based on truncation or on approximate summation of this...

Population Dynamics of Globally Coupled Degrade-and-Fire Oscillators

Synchronization Properties of Pulse-Coupled Resonate-and-Fire Neuron Circuits and Their Application

Introduction: Recent advances in neuroscience suggest that spiking neurons in cortical area are classified into two categories: integrators and resonators [1]. These neurons are different in the sensitivity to the timing of stimulus, and therefore show different synchronization properties in pulse-coupled systems. It is interested that the distribution of such neurons are layer-specific and dep...