Predictability and chaos in networks of integrate-and-fire neurons


Douglas Zhou

Courant Institute of Mathematical Sciences

New York University

    The conductance-based integrate-and-fire (I&F) model has successfully served as an efficient reduced Hodgkin-Huxley (HH) neuronal model to investigate spike-encoding properties of both single neuron and large-scale cortical networks due to less complexity and lower computational cost. One may ask whether there exists a fundamental difference in dynamics between the HH and I&F neuronal networks. Notably chaos can arise in the dynamics of both single HH neuron and networks. However, it has been proven that a single I&F neuron cannot be chaotic under any general time-dependent stimulus and it is an open problem whether an I&F network can be chaotic or not. More generally, for any given conductance-based I&F network with some sparsity and heterogeneous cortical connections, how to characterize its long time stability using Lyapunov exponents.
    In this talk, we address these issues and demonstrate that an all-to-all, homogeneously pulse-coupled I&F neuronal network can indeed give rise to chaotic dynamics under an external periodic current drive. We also provide a stable numerical method for the accurate evaluation of the spectrum of Lyapunov exponents for the I&F like neuronal network.