Adaptive estimation of firing patterns of Hindmarsh-Rose neurons and synchronization detection with instantaneous Lyapunov exponents

In this paper, we present an adaptive observer 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 an adaptive observer 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.