Thesis - Department of Electronic & Computer Engineering

⎛Given y, if A maxis the solution to I 2e y ---b I⎞⎜ 1– 1⎟= bA( e y/ A – 1), A maxis the⎝ ⎠upper limit of the pulse amplitude corresponding to y. The intersection ofA maxandAθ= ----- will give us the upper bound of θ, defined as θ h( T p) .T pConsider the extreme case when T pis very small ( 0 < T p« 1 );v 2I 2bA eT p ⁄ τ( – 1)– -------------------------e T ⁄ τ I– 1 2bA T p< – ------------------⁄ τe T ⁄ τ I– 1 2b θ -- 1= = – --------------------------τ θ( 1 – a)-------------------τIe 1– 1y( 1 – a)⎛ -------------------I⎞Define θ mas the solution to I 1( 1 – δ 1) e 1θ⎜ – 1⎟= by, where y = -- . Thus⎝ ⎠τθ mis the lower limiting of θ h( T p) .θ( 1 – a)⎛ -------------------τI⎞If θ l( T p) < θ< θ m, then I 2 ⎜e1– 1⎟≤ b θ for all .⎝ ⎠-- Tτ pFor a simple WTA model with a = b = 0.5 and I 1= 1.0, δ 1= 0.1 respectively,the necessary conditions for the network to exhibit WTA is given in Fig. 5.7.46