Did you tried a timing based rule? You can see an exemple of this law in Dayan and Abbott, 2001 (theoretical  neuroscience), figure 2.8. Basically, weigths depend on spike timing and not on firing rate. Spikes comming before lead to a strong depression and spike comming after to a strong potentiation.

Yes, I know that. It's STDP, but as I said in my question, the timing matters but only in a  certain range of firing rate. for example in some cases, it fails in more than 40 Hz , or less than 1 Hz . sometimes in high frequency of firing we only have potentiation independent of timing order of pre and post firing. Thus we can say it is not only depend on timing but also other factors like rate and cooperativity are important. It is well-known ( for example you can see http://www.ncbi.nlm.nih.gov/pubmed/11754844) , but I am sicking for a mathematical model for plasticity that involve all this factors.

Thanks for your answer.

In my opinion, the model that best captures all the induction phenomenologies of plasticity such as rate, timing, and cooperativity is the 2010 Clopath model ( http://www.ncbi.nlm.nih.gov/pubmed/20098420 ). If you also care about the locus of expression of plasticity (pre versus post), then I would say our very recent eLife paper provides the most complete model to date ( http://elifesciences.org/content/early/2015/08/26/eLife.09457 ). The vast majority of models default to synaptic gain change to model plasticity, but this is equivalent to saying that expression is postsynaptic only, which is wrong at many synapse types. Because presynaptic expression will have important implications for circuit dynamics, it is a bad idea not to model presynaptic long-term plasticity in recurrent network models of STDP. In the end, it all depends on what you wish to model. I quite like Pfisters triplet rule for its elegance and simplicity, but it doesn't capture all of the STDP phenomenology.

Thanks a lot, your explanations were really useful