Non-periodic responses of the Izhikevich neuron model to periodic inputs

Abstract

In the field of neuroscience, it is widely acknowledged that neurons exhibit periodic, quasi-periodic, and chaotic responses to periodic inputs. In this study, we evaluated the responses of the Izhikevich neuron model stimulated by sinusoidal inputs. First, we analyzed the dynamical behavior of the Izhikevich neuron model to the sinusoidal inputs in the state space and found two types of responses: periodic and non-periodic. Next, we obtained the domains of the periodic and non-periodic responses on the frequency-amplitude plane of the sinusoidal inputs by evaluating the diversity index of the inter-spike intervals. Finally, we analyzed the responses of the Izhikevich neuron model using the stroboscopic plot. Consequently, we clarified that a periodic response is a limit cycle and an irregular response is a torus, which implies that the irregular responses of the Izhikevich neuron model stimulated by sinusoidal inputs are quasi-periodic responses.

Rich spike patterns from a periodically forced Izhikevich neuron model

“…The v-nullcline, defined as dv dt = 0, is as follows: Likewise, the u-nullcline is given by u = bv. (10) Note that both can be expressed as a function u of v. The v-nullcline is a parabola that moves in the direction of the u axis accompanying the fluctuation of I AC in Eq. ( 3) and the u-nullcline is a straight line (see Fig.…”

“…Therefore, here, we carried out a comprehensive evaluation using a wider range of amplitude and period pairs. We have already investigated the responses of a regular spiking (RS) neuron of the model to sinusoidal input and identified periodic and quasi-periodic behavior [9,10]. However, much remains to be learnt about the non-periodic responses of other types of neurons to periodic inputs.…”

“…In the present study, we analyzed the responses of three other principal neuron types: fast spiking (FS) [11], intrinsically bursting (IB) [12], and chattering (CH) [12] neurons, as well as an RS neuron, in response to periodic forcing; and compared the results obtained for RS, FS, IB, and CH neurons.…”

Analysis on responses of chaotic Izhikevich neurons to periodic forcing

“…Previous researches [11][12][13][14][15][16][17][18][19][20][21] only investigated responses of periodic neurons stimulated by periodic forcing, while the present study investigates responses of chaotic neurons stimulated by periodic forcing. Then, in the present study, we used five parameter sets that reproduced the chaotic responses proposed by Izhikevich [10] and Naiki et al [23] and analyzed the responses of the chaotic Izhikevich neuron model stimulated by sinusoidal forcing with a focus on ISIs.…”

“…In addition, Nobukawa et al investigated the behavior of the model for weak sinusoidal stimulation [12,13]. In our previous studies, we analyzed responses by applying sinusoidal forcing to five principal types of Izhikevich neurons: regular spiking, fast spiking, intrinsically bursting, chattering, and low-threshold spiking [14][15][16][17][18][19][20][21]. Consequently, the coefficient of variation was high for regular responses and low for irregular responses.…”