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 a first-order passive decay model In the absence of external or neuronal stimuli the simplest activation dynamics model is Z (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 n since for any finite initial condition (t)=x1(0)e 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 assive-decay rate A.>0 scales the rate to the membrane 's resting potential solution: X(=X(0)6 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 : At i i i x t x e − （ ）= （0） Passive-decay rate measures: the cell membrane’s resistance or “friction” to current flow. i i i x = −A x •
property Pay attention to A 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