Stochastic Resonance(SR) is a phenomena that a excitable system is capable of detecting weak signal best with some optimal noise strength. In usually case, the optimal noise strength is only one value (one maximum in the S/N versus noise strength plot). Since our environment is always changing, a crucial problem is that is the noise strength always in this optimal level ? Namely, for different environment, thus different noise strength, does our system automatically tune the excitability such that it is optimal ? This means that we will have a flat plateau in the S/N versus noise strength plot(say, SR curve)! The motivation now is clear. We have developed a adaptive FitzHugh-Nagumo model that can tune its excitability. This model should have non-trivial behavior on SR and even Coherence Resonance (CR)! Therefore, let us see if there is some clues in the past research. In other words, what kind of system have a nontrivial SR curve.

A paper published at Nature in 1995 considered the signal passes many parallel FHN systems and sum up there responses as the output. There main finding is that when the number of parallel FHNs become large, there is a plateau in the SR curve! Also, these noise added will not affect the ability to detect supra-threshold signal. Another similar system published at Plos one in 2011 considered several independent noise sources producing Poisson firing by presynaptic neurons affect the postsynaptic neuron through TM dynamical synapse (with both synaptic depression and facilitation). And also added a weak signal to the postsynaptic neuron. The results showed that with these kind of “synaptic filter” tuning the noise effect. There will be two peaks in the SR curve and the place where peak happens can be tuned by changing the time scale of synaptic plasticity. These two systems with nontrivial SR curves are both “prefilter”-like. I also found two PRE papers which is more alike with our adaptive FHN system

One published in 2008 was Volman's previous work. They consider a random neural network with N neuron and the synaptic dynamic is the same as the bursting paper we are familiar with. There main founding is that asynchronous release, that is a dynamic-dependent noise source, will make the SR curve changes with N. And turns out to have optimal N and optimal asynchronous release strength g for weak signal detection. The other paper in 2014 was considering a different excitable system with positive feedback and negative feedback. They tried to work out the effect of this +/- feedback on “CR curve”, how coherence of the noise-driven activity versus the noise level. I think after analyzing the SR behavior of our adaptive FHN model, we can compare our results with these two models.

One can find the html I presented here : https://networks.tir.tw/~yjyang/present/GM1tuningSR.html

The four papers I mentioned in this talk are :

1. Nature 1995, Stochastic resonance without tuning, J.J. Collins et al.
2. Plos one 2011, Emergence of Resonances in Neural Systems:The interplay between Adaptive Threshold and Short-term Synaptic Plasticity, J.F. Mejias and J.J.Torres
3. PRE 2008, Activity-dependent stochastic resonance in recurrent neuronal network, V.Volman and H.Levine
4. PRE 2014, Event-triggered feedback in noise-driven phase oscillators, J.A. Kromer et al.