Membrane time Constants The membrane time constant c scales the time variable of the activation dynamical system The multiplicative constant model A (3-8) 2002.10.8
2002.10.8 Membrane Time Constants The membrane time constant scales the time variable of the activation dynamical system. The multiplicative constant model: Ci i i i xi C x = -A • （3－8）
Solution and property solution X()=x1(0)e I property The smaller the capacitance, the faster things change As the membrane capacitance increases toward positive infinity, membrane fluctuation slows to stop
Solution and property solution t C A i i i t x e − x ( ) = (0) i property The smaller the capacitance ,the faster things change As the membrane capacitance increases toward positive infinity,membrane fluctuation slows to stop
Membrane resting potentials Definition Define resting potential p as the activation value to which the membrane potential equilibrates in the absence of external or neuronal inputs a x: +p (3-11) Solutions x;(t)=x;(0e+1(1-e) (3-12) A 2002.10.8
2002.10.8 Membrane Resting Potentials Define resting Potential as the activation value to which the membrane potential equilibrates in the absence of external or neuronal inputs: Pi i i i i Ci x = -A x + P • Solutions (1- e ) A P x (t) x (0)e t C A - i i t C A - i i i i i i = + Definition (3-11) (3-12)
Note The capacitance appear in the index of the solution it is called time-scaling capacitance It does no affect the steady-state solution and does not depend on the finite initial condition In resting case we can find the solution quickly
Note The capacitance appear in the index of the solution,it is called time-scaling capacitance. It does no affect the steady-state solution and does not depend on the finite initial condition. In resting case,we can find the solution quickly
Additive External Input Add input Apply a relatively constant numeral input to a neuron Xi=-X;+1 (3-13) solution X(t)=x:(0)e+l1(1-e)(3-14)
Additive External Input Add input Apply a relatively constant numeral input to a neuron. i i xi = -x + I • solution x (t) x (0)e I (1- e ) -t i -t i = i + (3-13) (3-14)