In This Project You Will Investigate A Very Simple Model Of The Firing Mechanism Of A Neuron Here V Is The Membrane P 1 (58.19 KiB) Viewed 24 times
In This Project You Will Investigate A Very Simple Model Of The Firing Mechanism Of A Neuron Here V Is The Membrane P 2 (43.04 KiB) Viewed 24 times
In this project, you will investigate a very simple model of the firing mechanism of a neuron. Here, v is the membrane potential and u is the recovery current. The constant parameters are the membrane capacitance (C), the input current (1), the resting membrane potential (ur) and the instantaneous threshold potential (vt). The parameters k and b are determined by the neuron's rheobase and input resistance. (The full model has a cubic function of v, see e.g. www.scholarpedia.org/article/FitzHugh-Nagumo). odv = k(v – Vr)(v – V+) – u + I vrvt- = b(v – Vr) – u. dt dt du
1. If C, 1, Ur, Vt, k and b are assumed to be nonzero, show that one can work with a 3- dimensional parameter space (instead of 6-dimensional) by transforming to new vari- ables in which the system becomes: dv du 12 + av – u +8 = βυ – μ. dt dt Hint: consider new variables ū = V(v – vr) and ū= Uu, and choose the constants U and V appropriately. [2 marks] =
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