Estimation of connections in a hybrid neuronal network

Abstract

The paper describes a new method of reconstructing the connections in a neuronal network based on a simulation using the Izhikevich hybrid model of a neuron expressed by nonlinear differential equations with jump discontinuities. The estimation of synaptical connections is accomplished by using an Unscented Kalman Filter to first synchronize the spiking in the network model with the observed impulses in membrane potentials and then using the recursive least-squares method to estimate the strength of each connection. The algorithm was tested on data generated by the Hodgkin-Huxley models and Hindmarsh-Rose models. The algorithm produced results for networks of sizes up to 70 neurons, and was able to accurately capture and track the changes in the connectivity.