Methods in Neuronal Modeling: From Ions to Networks
Methods in Neuronal Modeling: From Ions to Networks
Dynamics and bifurcations of the adaptive exponential integrate-and-fire model
Biological Cybernetics - Special Issue: Quantitative Neuron Modeling
Simple model of spiking neurons
IEEE Transactions on Neural Networks
Which model to use for cortical spiking neurons?
IEEE Transactions on Neural Networks
On the simulation of nonlinear bidimensional spiking neuron models
Neural Computation
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The quadratic adaptive integrate-and-fire model (Izhikevich, 2003, 2007) is able to reproduce various firing patterns of cortical neurons and is widely used in large-scale simulations of neural networks. This model describes the dynamics of the membrane potential by a differential equation that is quadratic in the voltage, coupled to a second equation for adaptation. Integration is stopped during the rise phase of a spike at a voltage cutoff value Vc or when it blows up. Subsequently the membrane potential is reset, and the adaptation variable is increased by a fixed amount. We show in this note that in the absence of a cutoff value, not only the voltage but also the adaptation variable diverges in finite time during spike generation in the quadratic model. The divergence of the adaptation variable makes the system very sensitive to the cutoff: changing Vc can dramatically alter the spike patterns. Furthermore, from a computational viewpoint, the divergence of the adaptation variable implies that the time steps for numerical simulation need to be small and adaptive. However, divergence of the adaptation variable does not occur for the quartic model (Touboul, 2008) and the adaptive exponential integrate-and-fire model (Brette & Gerstner, 2005). Hence, these models are robust to changes in the cutoff value.