Firing Pattern Estimation of Synaptically Coupled Hindmarsh-Rose Neurons and Synchronization Dection by Instantaneous Lyapunov Exponents

Abstract

In this report, we present adaptive observers for synaptically coupled Hindmarsh-Rose (HR) neurons with the membrane potential measurement under the assumption that some of parameters in an individual HR neuron are known. Using the adaptive observers for a single HR neuron, we propose a two-stage merging procedure to identify the firing pattern of a model of synaptically coupled HR neurons. The procedure allows us to recover the internal states and to distinguish the firing patterns of the synaptically coupled HR neurons, with early-time dynamic behaviors.