Jump and Decay

This response function produces an instantaneous jump in the post-synaptic response equal to the synaptic strength, followed by an exponential decay back to a baseline response at a rate proportional to the time constant.

\[\large PSR(t)_{ij} = w_{ij}e ^ \left({\Delta_t} / {\tau} \right) + b\]

Where \(PSR(t)_{ij}\) is the post-synaptic response of the synapse connecting neuron \(j\) to \(i\), \(w_{ij}\) is the synaptic strength, \(\Delta_t\) is the difference between time of the last spike at neuron \(j\) and the current time, \(\tau\) is the decay time constant, and \(b\) is the baseline value that \(PSR_{ij}\) decays to over time.

All spike responders use the incoming synaptic strength as the jump height.

• Base-Line: The post-synaptic response value when no spikes have occurred. Alternatively, the post-synaptic response to which the spike responder decays over time.

• Time Constant: Time constant of decay (ms). Roughly the time it takes to decay to near-baseline. Larger time constants produce slower decay.

• Use Convolution: If true the current spike response adds the PSR from the previous iteration, which smoothes out the response.