Distribution of spiking and bursting in Rulkov’s neuron model

Abstract Large-scale brain simulations require the investigation of large networks realistic neuron models, usually represented by sets differential equations. Here we report a detailed fine-scale study dynamical response over extended parameter ranges computationally inexpensive model, two-dimensional Rulkov map, which reproduces well spiking and spiking-bursting activity real biological neurons. In addition, provide evidence existence nested arithmetic progressions among periodic pulsing bursting phases Rulkov’s neuron. We find that specific remarkably complex sequences neural oscillations can be expressed as simple linear combinations pairs certain basal periodicities. Moreover, such are robust observed abundantly in diverse control planes described detail. believe findings to add significantly knowledge dynamics potentially helpful large-scale other networks.