Mode-locking behavior of Izhikevich neurons under periodic external forcing

Many neurons in the auditory system of the brain must encode periodic signals. These neurons under periodic stimulation display rich dynamical states including mode locking and chaotic responses. Periodic stimuli such as sinusoidal waves and amplitude modulated sounds can lead to various forms of n:m mode-locked states, in which a neuron fires n action potentials per m cycles of the stimulus. Here, we study mode-locking in the Izhikevich neurons, a reduced model of the Hodgkin-Huxley neurons. The Izhikevich model is much simpler in terms of the dimension of the coupled nonlinear differential equations compared with other existing models, but excellent for generating the complex spiking patterns observed in real neurons. We obtained the regions of existence of the various mode-locked states on the frequency-amplitude plane, called Arnold tongues, for the Izhikevich neurons. Arnold tongue analysis provides useful insight into the organization of mode-locking behavior of neurons under periodic forcing. We find these tongues for both class-1 and class-2 excitable neurons in both deterministic and noisy regimes.