Arnold tongues and the Devil's Staircase in a discrete-time Hindmarsh–Rose neuron model

Abstract We investigate a three-dimensional discrete-time dynamical system, described by a three-dimensional map derived from a continuous-time Hindmarsh–Rose neuron model by the forward Euler method. For a fixed integration step size, we report a two-dimensional parameter-space for this system, where periodic structures, the so-called Arnold tongues, can be seen with periods organized in a Farey tree sequence. We also report possible modifications in this parameter-space, as a function of the integration step size.