DOI: 10.1142/S0217979211100266 International Journal of Modern Physics B Vol. 25, No. 12 (2011) 1653–1670 c  World Scientific Publishing Company TRANSITION OF SPIRAL WAVE IN A MODEL OF TWO-DIMENSIONAL ARRAYS OF HINDMARSH ROSE NEURONS JUN MA School of Sciences, Lanzhou University of Technology, Lanzhou 730050, China Key Laboratory of Gansu Advanced Control for Industrial Processes, Lanzhou 730050, China hyperchaos@163.com YA JIA Department of Physics, Central China Normal University, Wuhan 430079, China jiay@phy.ccnu.edu.cn CHUN-NI WANG School of Sciences, Lanzhou University of Technology, Lanzhou 730050, China WU-YIN JIN College of Mechano-Electronic Engineering, Lanzhou University of Technology, Lanzhou 730050, China Received 13 August 2008 Revised 3 October 2008 In this paper, the condition of completely nearest-neighbor couplings is introduced into the coupled Hindmarsh–Rose neurons in two-dimensional arrays. It is found that the stable rotating spiral wave can be developed and the transition of spiral wave in the coupled Hindmarsh–Rose neurons are investigated. The factor of synchronization is de- fined to investigate the development and instability of the spiral wave. Furthermore, the external injected current, coupling coefficients and other decisive bifurcation parameter r and χ, are endowed with different values to study the transition of spiral wave by analyzing the factor of synchronization and the snapshots of the activator. It is found that the critical sudden change points in the curve for factor of synchronization often indicates sudden transition of spiral wave, the instability or death of the spiral wave. The snapshots are also plotted to confirm the results from the curve of the factor of synchronization. Finally, the noise-induced instability and chaotic logistic map-induced instability of spiral wave are investigated and discussed. Keywords : Spiral wave, Hindmarsh–Rose neurons; instability; factor of synchronization. PACS numbers: 47.54.-r, 05.45.-a 1653