Eur. Phys. J. Special Topics 227, 821–835 (2018)
https://doi.org/10.1140/epjst/e2018-800006-2

Regular Article

Spatial patterns in a network composed of neurons with different excitabilities induced by autapse

¹ School of mathematics and statistics, Chifeng University, Chifeng 024000, P.R. China
² Institute of applied mathematics, Chifeng University, Chifeng 024000, P.R. China
³ Department of Physiology and Biophysics, School of Life Sciences, Fudan University, Shanghai 200438, P.R. China

^a e-mail: liyuye2000@163.com

Received: 19 January 2018
Received in final form: 22 March 2018
Published online: 19 October 2018

Abstract

It has been identified that autapse can modulate dynamics of single neurons and spatial patterns of neuronal networks. In the present paper, based on the results that autapse can induce type II excitability changed to type I excitability, spatial pattern transitions are simulated in a two-dimensional neuronal network composed of excitatory coupled neurons with autapse which can induce excitability transition. Different spatial patterns including random-like pattern, irregular wave, regular wave, and nearly synchronous behavior are simulated with increasing the percentage (σ) of neurons with type I excitability. When noise is introduced, spiral waves are induced. By calculating signal-to-noise ratio from the spatial structure function and the mean firing probability of neurons, regular waves and spiral waves exhibit optimal spatial correlation, implying the occurrence of spatial coherence resonance phenomenon. The changes of mean firing probability of neurons show that different firing frequency between type I excitability and type II excitability may be an important factor to modulate the spatial patterns. The results are helpful to understand the spatial patterns including spiral waves observed in the biological experiment on the rat cortex perfused with drugs which can induce single neurons changed from type II excitability to type I excitability and block the inhibitory couplings between neurons. The excitability transition, absence of inhibitory coupling, noise as well as the autapse are important factors to modulate the spatial patterns including spiral waves.