Physica A 387 (2008) 4404–4410 www.elsevier.com/locate/physa Synchronization transition in gap-junction-coupled leech neurons ✩ Qingyun Wang a,b , Zhisheng Duan a , Zhaosheng Feng c,∗ , Guanrong Chen a,d , Qishao Lu e a National Key Laboratory for Turbulence and Complex Systems College of Engineering, Peking University, Beijing 100871, China b School of Stat. & Math., Inner Mongolia Finance and Economics College, Huhhot 010051, China c Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78539, USA d Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China e School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China Received 5 November 2007; received in revised form 28 January 2008 Available online 29 February 2008 Abstract Real neurons can exhibit various types of firings including tonic spiking, bursting as well as silent state, which are frequently observed in neuronal electrophysiological experiments. More interestingly, it is found that neurons can demonstrate the co-existing mode of stable tonic spiking and bursting, which depends on initial conditions. In this paper, synchronization in gap-junction- coupled neurons with co-existing attractors of spiking and bursting firings is investigated as the coupling strength gets increased. Synchronization transitions can be identified by means of the bifurcation diagram and the correlation coefficient. It is illustrated that the coupled neurons can exhibit different types of synchronization transitions between spiking and bursting when the coupling strength increases. In the course of synchronization transitions, an intermittent synchronization can be observed. These results may be instructive to understand synchronization transitions in neuronal systems. c  2008 Elsevier B.V. All rights reserved. PACS: 05.45.-a; 05.65.+b; 05.45.Xt. Keywords: Coupled neurons; Synchronization transition; Oscillation; Leech neuron model; Bifurcation diagram 1. Introduction Synchronization of a set of interacting individuals or units has been intensively studied because of its ubiquity in the natural world [1]. The synchronization of neuronal signals has been proposed as one of the mechanisms to transmit and code information in the human brain [2,3]. Mammalian nervous systems exhibit a diversity of synchronized behaviors including periodic, quasi-periodic, chaotic, noise-induced and noise-enhanced synchronous rhythms [4–8]. It was suggested that theoretical studies of such synchronized behaviors in neuronal assemblies play an ✩ This work is supported by NSF of China under Grants 10702023, 60674093 and 10432010, and partially supported by China Post-doctoral Grant 20070410022. ∗ Corresponding author. Tel.: +1 956 292 7483; fax: +1 956 381 5091. E-mail address: zsfeng@utpa.edu (Z. Feng). 0378-4371/$ - see front matter c  2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physa.2008.02.067