@article{KomarovBazhenov2016, author = {Komarov, Maxim and Bazhenov, Maxim}, title = {Linking dynamics of the inhibitory network to the input structure}, series = {Journal of computational neuroscience}, volume = {41}, journal = {Journal of computational neuroscience}, publisher = {Springer}, address = {Dordrecht}, issn = {0929-5313}, doi = {10.1007/s10827-016-0622-8}, pages = {367 -- 391}, year = {2016}, language = {en} } @article{KrishnanBazhenovPikovskij2013, author = {Krishnan, Giri Panamoottil and Bazhenov, Maxim and Pikovskij, Arkadij}, title = {Multipulse phase resetting curves}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {88}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {4}, publisher = {American Physical Society}, address = {College Park}, issn = {1539-3755}, doi = {10.1103/PhysRevE.88.042902}, pages = {9}, year = {2013}, abstract = {In this paper, we introduce and study systematically, in terms of phase response curves, the effect of dual-pulse excitation on the dynamics of an autonomous oscillator. Specifically, we test the deviations from linear summation of phase advances resulting from two small perturbations. We analytically derive a correction term, which generally appears for oscillators whose intrinsic dimensionality is >1. The nonlinear correction term is found to be proportional to the square of the perturbation. We demonstrate this effect in the Stuart-Landau model and in various higher dimensional neuronal models. This deviation from the superposition principle needs to be taken into account in studies of networks of pulse-coupled oscillators. Further, this deviation could be used in the verification of oscillator models via a dual-pulse excitation.}, language = {en} }