2_26_09_ExcitatoryInhibitoryNetworks

2_26_09_ExcitatoryInhibitoryNetworks - Outline of the...

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Outline of the Lecture Outline of the Lecture Excitatory-inhibitory Network Models  Excitatory-inhibitory Network Models  Non-symmetric Matrices         Phase Plane          Olfactory  Non-symmetric Matrices         Phase Plane          Olfactory  Bulb Bulb    
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Recurrent Networks with  Recurrent Networks with  Non-symmetric Matrices  Non-symmetric Matrices  May Exhibit Oscillations May Exhibit Oscillations    
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A recurrent network is a feedforward network with a recurrent synaptic weight matrix.
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For symmetric M, the eigenvectors are orthonormal, i.e. , and general solutions have time constants τ r /(1- λ r ) : τ r d v dt = M - I ( v + h v t ( 29 = χ μ τ ( 29 ε μ μ =1 Ν μ χ υ τ ( 29 = ε υ η 1- λ υ 1- ε - τ 1- λ υ ( 29 τ ρ + χ υ 0 ( 29 ε - τ 1- λ υ ( 29 τ ρ r e μ ρ ε υ = δ μυ
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For a feedforward network: For a recurrent network: τ r dv a dt = - v a + F W ab b =1 N a å u b æ è ç ö ø ÷ æ è ç ö ø ÷ τ r d r v dt = - r v + F W × r u ( ) τ r d r v dt = - r v + F W × r u + M × r v ( )
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