Chapter 3.Neuronal Dynamics 2 Activation Models 3.1 Neuronal dynamical system Neuronal activations change with time.The way they change depends on the dynamical equations as following: ●】 x=g(FX,Fy,…〉 (3-1) y=h(Fx,Fy,…) (3-2) 2002.10.8
2002.10.8 Chapter 3. Neuronal Dynamics 2 :Activation Models Neuronal activations change with time. The way they change depends on the dynamical equations as following: x = g（FX ，FY ，） • y = h（FX ，FY ，） • (3-1) (3-2) 3.1 Neuronal dynamical system
3.1 ADDITIVE NEURONAL DYNAMICS first-order passive decay model In the absence of external or neuronal stimuli, the simplest activation dynamics model is: xi=一xi (3-3) (3-4) 2002.10.8
2002.10.8 In the absence of external or neuronal stimuli, the simplest activation dynamics model is: i xi = −x • y j = −yj • 3.1 ADDITIVE NEURONAL DYNAMICS (3-3) (3-4) first-order passive decay model
3.1 ADDITIVE NEURONAL DYNAMICS since for any finite initial condition x,(t)=x,(0)et The membrane potential decays exponentially quickly to its zero potential
t xi t xi e − ( ) = (0) since for any finite initial condition 3.1 ADDITIVE NEURONAL DYNAMICS The membrane potential decays exponentially quickly to its zero potential
Passive Membrane Decay Passive-decay rate ,>0 scales the rate to the membrane's resting potential. ● xi=-AjXi solution x,(t)=x,(0)e4 Passive-decay rate measures:the cell membrane's resistance or "friction"to current flow. 2002.10.8
2002.10.8 Passive Membrane Decay Passive-decay rate Ai 0 scales the rate to the membrane’s resting potential. solution : Passive-decay rate measures: the cell membrane’s resistance or “friction” to current flow. i i i x = −A x • A t i i i x t x e − （ ）= （0）
property Pay attention to 4;property The larger the passive-decay rate,the faster the decay--the less the resistance to current flow
Ai The larger the passive-decay rate,the faster the decay--the less the resistance to current flow. Pay attention to property property