Membrane Time Constants The membrane time constant C scales the time variable of the activation dynamical system. The multiplicative constant model: ● Cixi=-AiXi (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 i C x = -A x • （3－8）
Solution and property ■solution x;(t)=x,(0)e 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: Cixi=-Aixi+Pi (3-11) Solutions 0x0e产e (3-12) 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 not affect the asymptotic or steady-state solutionand does not depend on the finite initial condition
Note The capacitance appear in the index of the solution, it is called time-scaling capacitance. It does not affect the asymptotic or steady-state solution and does not depend on the finite initial condition. i i A P
Additive External Input Add input Apply a relatively constant numeral input to a neuron. ● Xi=-Xi+li (3-13) solution x()=x;(0)et+I(1-et) (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)