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Mode-locking behavior of Izhikevich neurons under periodic external forcing
BMC Neuroscience volume 16, Article number: P140 (2015)
Many neurons in the auditory system of the brain must encode amplitude variations of a periodic signal. These neurons under periodic stimulation display rich dynamical states including mode-locking and chaotic responses . Periodic stimuli such as sinusoidal waves and amplitude modulated (AM) sounds can lead to various forms of n:m mode-locked states, similar to the mode-locking phenomenon in a LASER resonance cavity. Obtaining Arnold tongues provides useful insight into the organization of mode-locking behavior of neurons under periodic forcing. In this study we obtained the regions of existence of various mode-locked states on the frequency-amplitude plane, which are called Arnold tongues, for Izhikevich neurons (see Figure 1). This study is based on the model for neurons by Izhikevich (2003), which is a reduced model of a Hodgkin-Huxley neuron . This model is much simpler in terms of the dimension of the coupled non-linear differential equations compared to other existing models, but excellent for generating the complex spiking patterns observed in real neurons . Hence we can describe the construction of harmonic and sub-harmonic responses in the early processing stages of the auditory system, such as the auditory nerve and cochlear nucleus.
Different mode-locked regions that are shown in the Arnold tongues diagram are predictors of mode-locking of auditory system neurons to sound, which in turn predict the formation of harmonics and sub-harmonics of the sound in the brain.
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Izhikevich Eugene : Dynamical Systems in Neurosceince: The geometry of Excitability and Bursting. 2007, Cambridge, Massachusetts: The MIT Press
Kim Youngtae: Identification of Dynamical States in Stimulated Izhikevich Neuron Models by Using a 0-1 Test. Journal of Korean Physical Society,. 2010, 57 (6): 1363-1368.
This work was supported by University of Connecticut College of Liberal Arts and Sciences.