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neurohw3 - 1 0.04 0.02 0 0.02 0.04 0.06 0.08 0 0.05 0.1...

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1. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 T, V1 Frequency = 37 * 2 spikes per second or 74 hz Period = 1/frequency = 1/74
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0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 T, V2 Frequency = 37 * 2 spikes per second or 74 hz Period = 1/frequency = 1/74 The same as neuron 1 b/c it is the same model with the same starting conditions and without coupling
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2. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -0.1 0 0.1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.2 0.4 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -0.1 0 0.1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.2 0.4 Tsyn = 1ms From top to bottom: (t, V1), (t, syn1), (t, V2), (t, syn2)
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0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -0.1 0 0.1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.5 1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -0.1 0 0.1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.5 1 Tsyn = 10ms From top to bottom: (t, V1), (t, syn1), (t, V2), (t, syn2) If tsyn is low than the syn values effectively spike just after a spike in the neuron occurs and rapidly fall back to zero. However if the tsyn is large enough (here 10ms) the fall back to zero is not fast enough to reach zero before another spike occurs, pushing the syn value up further and further with each spike, until a new high syn average steady state value is achieved. As syn increases the size of the kicks decrease until they equal the decrease caused by natural exponential decay, there the syn oscillates closely around a new high average value.
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3. For -60 mV, -60 mV see above graphs, the oscillations are in phase with each other. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -0.1 -0.05 0 0.05 0.1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.2 0.4 0.6 0.8 For -60mV (in blue) and -40mV (in red) Top of both graphs is t, v and bottom is t, syn The -40mV neuron lags behind the -60mV neuron in both the voltage and syn values. It is slightly negatively out of phase because it started at a higher voltage, which meant current had to be applied longer until it reached the spiking threshold.
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0.162 0.164 0.166 0.168 0.17 0.172 0.027 0.028 0.029 0.03 0.031 0.222 0.224 0.226 0.228 0.23 0.232 0.775 0.78 0.785 0.79 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -0.1 -0.05 0 0.05 0.1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.2 0.4 0.6 0.8
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For -60mV (in blue) and -80mV (in red) The Opposite effect occurs because the voltage is now lower requiring less current to be applied, however the overall phase shift (laterally) is reduced because once the neuron starting spiking the starting voltage quickly becomes less important. Top of both graphs is t, v and bottom is t, syn 4. 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.005 0.01 0.015 0.02 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.32 0.33 0.34 0.35 0.36 0.37
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0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -0.1 -0.05 0 0.05 0.1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.1 0.2 0.3 0.4 Neuron 1 is in blue and starts at -60 mV, 2 is in red and starts at -75mV. Top of both graphs is t, v and bottom is t, syn When fast excitatory coupling occurs the neurons push each other to fire at the same time and overcome any phase shifting introduced by the initial starting voltages. However the maximum peak on each spike reached by a neuron oscillates between the 2 as evidenced in the graph.
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5. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -0.1 -0.05 0 0.05 0.1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.1 0.2 0.3 0.4 Neuron 1 is in blue and starts at -60 mV, 2 is in red and starts at -75mV. Top of both graphs is t, v and bottom is t, syn When slower excitatory coupling occurs the neurons still fire together and the syn graph resembles that of the fast coupling graph. However since the neurons spike together and drive syn upward, they also oppose the decay back down (by external current) to the spiking threshold. Thus the spike is very fast once the threshold is reached, but the
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