Integrate-and-fire models capture the essence of the electrical activity a generic neuron, besides being more interesting from the computational point-of-view when compared to higher dimensional models such as the Hodgkin-Huxley one. In this project, we propose a new integrate-and-fire model described by a generalized Langevin equation that takes into account memory effects and additive or/and multiplicative colored noise. This more realistic and general approach has as a limit case the usual, memoryless and with delta-correlated Gaussian noise, stochastic integrate-and-fire model. Based on the proposed model, we will focus on the study of two remarkable phenomena of relevance in neuroscience: stochastic ressonance and the bifurcation process responsible for neural excitability. Within the first theme, we want to answer the following question: Is the stochastic ressonance a phenomenon intrinsic to neural dynamics, in other words, does this mechanism survive a more realistic formulation of neuron dynamics, asthe one given by the proposed model, or is it an artificial consequence of the oversimplification that characterizes memoryless models? Under the second theme, we want to know how the presence of colored noise and memory effects affect the dynamics near a bifurcation. We will study in detail the behavior of the non-Markovian system near the typical bifurcations of biophysical interest: saddle-node, saddle-node on invariant circle, subcritical Andronov-Hopf and supercritical Andronov-Hopf bifurcation. Besides addressing these two central problems, this project aims at establishing the regime of validity of the Markovian approximation given a set of parameters that characterizes the system and the environment.
News published in Agência FAPESP Newsletter about the scholarship: