1. A Return Map of the Spiking Neuron Model Yen-Chung Chang (Dep. of Life Science, NTHU) Xin-Xiu Lin Sze-Bi Hsu (Dep. of Math, NTHU) Shu-Ming Chang

2. 2 Outline Neurons, Spike,… Leaky Integrate-and-Fire Model Return Map

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11. Leaky Integrate-and-Fire Model

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13. 13 Leaky Integrate and Fire  m V / = I + V rest -V + F ex (t)(E ex -V) + F in (t)(E in -V) I ~ injected current V ~ Voltage F ~ inhibitory and excitatory conductance E ~ reversal potential  m ~ membrane potential decay constant

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16. Return Map

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20. 20 References W. Gerstner and W. M. Kistler, Spiking Neuron Models: Single Neurons, Populations, Plasticity, Cambridge University Press, 2002. G. Bi and M. Poo, Synaptic Modifications in Cultured Hippocampal Neurons: Dependence on Spike Timing, Synaptic Strength, and Postsynaptic Cell Type, J Neurosci., 18(24) (1998), 10464-10472. R. E. Mirollo and S. H. Strogatz, Synchronization of Pulse-Coupled Biological Oscillators, SIAM J. Appl. Math., 50 (1990), 1645-1662.