Fundamental limits of forced asynchronous spiking with integrate and fire dynamics
The authors consider a pair of leaky integrate-and-fire neurons, coupled with delta function synapses. The neurons have a common input current (multiplied by different magnitudes for the two neurons) which is used to control their dynamics. The authors consider three different types of objective in terms of neuron firing order and timing, and for each determine whether an input current can achieve the objective, and if so what is the optimal input current. The first objective is to fire neuron 1 but not neuron 2, in minimum time, from a (largely) arbitrary initial condition. The second objective is to fire a sequence of \(M\) spikes, where each spike is labeled by the neuron which fires it, again in minimum time. The third objective is to fire a sequence of \(M\) spikes, where each spike is labeled by both the neuron which fires it, and the time at which it occurs. Here, the sum of the squares of the differences between the difference between successive firing times and the difference between target firing times is to be minimized. A number of numerical examples are given, and robustness to disturbance and noise is considered.
scientific article; zbMATH DE number 6909824