Parameter and input estimation in Hindmarsh-Rose neuron by adaptive observer

In this paper, we present adaptive observers of Hindmarsh-Rose (HR) neurons with the membrane potential measurement under the assumption that all parameters in an individual HR neuron are unknown. Using the time-varying adaptive observer for MIMO systems, we propose two adaptive observers 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.