Thesis - Department of Electronic & Computer Engineering

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5.4 Examples of Pulse Coupled RealizationWithout considering implementation issues, we assume the capacity of the pulsebased communication is infinite, such that all the pulses can be put through.Let us look at the two-neuron model first. To make sure the recurrent strengths arechosen such that the system works at the WTA region, we choose a = b = 0.5 ,θ = 0.4τ , A = 4 and T p= 0.1τ , then we will get a concrete WTA model:τv˙ 1() t = – v 1() t + I 1+ 0.5s 1() t – 0.5s 2() tτv˙ 2() t = – v 2() t + I 2– 0.5s 1() t + 0.5s 2() twhere s 1 () t and s 2 () t follow the definition in section 5.1.With the same input conditions as the example analyzed in Chapter 2, whereI 1= 1.0, δ 1= 0.1 ⇒ I 2= 0.9 and τ = 1ms, according to the previous analysis andsimulation, with continuous model at steady states, we have˜ I 1 1.0= ----------- = --------------- = 2.0, v ˜, .1 – a 1 – 0.52 = 0 t s ≈ 19msv 140
The computer simulation results for this pulse coupled model are depicted in Fig.5.4.2.5Neural activities V.S. time2The winnerNeural activities1.510.5The loser00 5 10 15 20 25 30TimeFig. 5.4 The pulse coupled realization compared with the continuousIn this example, we can observe that the pulse coupled network preserves the samecompetitive behavior as the continuous network. “It shows nicely that informationabout a time dependent signal can indeed be conveyed by spike timing [12].” In thiscase, the temporal average of the outputs are very close to the outputs of the continuousmodel. Consequently it is possible to retain all the desirable properties of the continuousnetwork with pulse coupled realizations.However, if we choose θ = 0.8τ , A = 8 and T p = 0.1τ instead, the pulse coupledmodel does not exhibit the same competitive behavior any more, as shown in Fig.5.5.41
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: the network will either work at WTA
Page 43 and 44: 5.5 Steady State AnalysisAs demonst
Page 45 and 46: all the losers. To ensure that all
Page 47 and 48: 10090θ=θ mThe necessary condition
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
Page 57 and 58: cell will never collide with each o
Page 59 and 60: ps ( i) = ( 1 - ϕ i)δ( s)for s =
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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