BioSystems 88 (2007) 127–136 Robustness and regularity of oscillations in neuronal populations Xi Shen a, ∗ , Philippe De Wilde b a Department of Electrical and Electronic Engineering, Imperial College London, South Kensington Campus, Exhibition Road, London SW7 2BT, UK b Department of Computer Science, Heriot-Watt University, Edinburgh EH14 4AS, UK Received 14 October 2005; received in revised form 4 April 2006; accepted 12 May 2006 Abstract We study a biologically plausible but computationally simplified integrate-and-fire neuronal model. Oscillatory activity is analyzed in the networks with and without self-connections. We perform a detailed scan of four major parameters that represent the properties of neurons and synapses: connection ratio, connection strengths, post-synaptic potential decay rate and soma’s potential decay rate. It is observed that networks with different properties exhibit different periods and different patterns of synchrony. We find that generally these oscillations are robust against changes of parameters, meanwhile we also locate the parametric boundaries where oscillations break down. © 2006 Elsevier Ireland Ltd. All rights reserved. Keywords: Integrate-and-fire model; Oscillations; Robustness 1. Introduction In the past decade, oscillatory activity has received much attention in both neurophysiological and dynami- cal systems research. Although it is still uncertain how information is coded in oscillations, multiple experimen- tal discoveries and simulation results do suggest that os- cillatory behavior plays an important role in many func- tions that are carried out by the brain. When synchronized firing with a precision in the mil- lisecond range was observed in the visual cortex (Gray et al., 1989), there was a direct implication that oscillatory activity might be wide-spread and essential in the brain. After that, many experiments confirmed the ubiquity of synchronization (see Kreiter and Singer, 1996; Brecht et al., 1998), and implications were made from a neu- roscience point of view (Singer, 1999). Meanwhile, in ∗ Corresponding author. Tel.: +44 20 75946331; fax: +44 20 75946274. E-mail address: xi.shen@imperial.ac.uk (X. Shen). computational neuroscience research, neuronal models were built to investigate synchronous and oscillatory be- havior (see Aertsen et al., 1996; Coombes, 2003). Some of these studies focused on neural oscillators which in- volve only one or several pairs of neurons (Aoyagi et al., 2003; Nomura and Aoyagi, 2005), while others were conducted in the framework of neural networks (Brunel, 2000; Borisyuk, 2002). Due to their physiological plausibility and compu- tational simplicity, integrate-and-fire (IF) models are widely used for simulating neuronal populations (Perkel, 1976). In the paper of Borisyuk (2002), oscillatory ac- tivity was investigated using a detailed integrate-and-fire model with signal propagation delay and refractory peri- ods taken into account. Although oscillatory activity was observed with various parametric settings, it is not clear when the oscillations start to break down and how robust they are against fluctuations in parameters. In this paper, we describe a simplified but realistic integrate-and-fire model and use this model to investigate the oscillatory behavior of a large neuronal population. 0303-2647/$ – see front matter © 2006 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.biosystems.2006.05.002