Thesis - Department of Electronic & Computer Engineering

all the losers. To ensure that all the losers remain silent in steady states, their peak valuesshould be always below zero. As illustrated in the appendix, we obtainv i I i bA eT p ⁄ τ( – 1)= – -------------------------⁄ ,– 1e T τwhich has to satisfy v i≤ 0 , since v 2is the neuron with the second largest input, thecondition becomes v 2≤ 0 .(v 2 I 2 bA ey / A – 1)= – ------------------------------- , where yy( 1 – a)⎛ -------------------I⎞⎜e1– 1⎟⎝ ⎠=θ--τIf the right hand side of the inequality is greater than zero,⎛I 2 ⎜e⎝y( 1 – a)-------------------I 1⎞– 1⎟⎠> bA( e y/ A – 1).That is, whenθ--τis greater than certain value, even if it reaches the steady state, whateverthe pulse form is, it will not stay at the steady state.θSuppose a + b = 1 holds, and let y denote -- , the necessary condition for the networkto exhibit WTA behaviorτis⎛I 2 ⎜e⎝-----ybI 1⎞– 1⎟≤ bA( e y/ A – 1).⎠45