Thesis - Department of Electronic & Computer Engineering

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⎛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
10090θ=θ mThe necessary conditions to exhibit WTATp=0.018070Pulse amplitude605040WTAWSA30Tp=0.052010Amin00 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2Threshold(Normalized)Fig. 5.7 The necessary conditions to exhibit WTA. The non-shaded area is the regionwhich can exhibit WTA behavior, while the shaded area is inhibited can not exhibitWTA behavior.For a fixed, to make the pulse coupled network exhibit WTA behavior, on oneT phand, the pulse amplitude A must be greater than A min , the intersection of the twoθlines A = A minand A = ----- determines the lower bound of the threshold θ l ( T p );T pone the other hand, A must be less than , the intersection of the curve and theA maxT pθline A = ----- determines the upper bound of θ h ( T p ). Only when the threshold is chosensuch thatθ l ( T p ) < θ
Page 3 and 4: the system level. Our results show
Page 5: activities. The basin of attraction
Page 9 and 10: It is interesting to note that whic
Page 11 and 12: Although there is no saturation in
Page 13 and 14: • Response time of the system;As
Page 15 and 16: e verified by computer simulation (
Page 17 and 18: inhibition. Due to the fact that ea
Page 19 and 20: tion. Thus the power consumption is
Page 21 and 22: Let∆be the minimum time necessary
Page 23 and 24: The sender initiates the sequence b
Page 25 and 26: Here in Table 1 is the comparison o
Page 27 and 28: source cell will be broadcast on th
Page 29 and 30: At this point, it seems appropriate
Page 31 and 32: detected, all the potential spikes
Page 33 and 34: InitializationFor each timestep ε
Page 35 and 36: global inhibition BusActivity to fr
Page 37 and 38: Spikes from the winnerATpTTT n T n+
Page 39 and 40: the network will either work at WTA
Page 41 and 42: The computer simulation results for
Page 43 and 44: 5.5 Steady State AnalysisAs demonst
Page 45: all the losers. To ensure that all
Page 49 and 50: 100Necessary conditions to exhibit
Page 51 and 52: The response time is estimated in t
Page 53 and 54: 5.6.2 Further study on the non-arbi
Page 55 and 56: 100Response time V.S. equivalent ga
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Page 61 and 62: These results show that the collisi
Page 63 and 64: 5.7.4 SummaryCompared with the Pois
Page 65 and 66: 6. ConclusionsIn this thesis, a cla
Page 67 and 68: In this thesis, we consider only a
Page 69 and 70: v i() t≤I i----------- ( 1 - e1 -
Page 71 and 72: If a+ b - 1≥0, then τ---- d [ v
Page 73 and 74: If a+ b - 1 > 0, since v i() t > 0
Page 75 and 76: whereV ˙ i () t=max( v i ()0 t , )
Page 77 and 78: θ t s Nf f wp ct(%) p cl(%) p cw(%
Page 79 and 80: 10. “WTA networks with lateral ex

Thesis - Department of Electronic & Computer Engineering

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