Adaptive Synchronization of Two Coupled Hindmarsh-Rose Neurons with Fully Unknown Parameters

The goal of this paper is to present an adaptive controller to synchronize two Hindmarsh-Rose neurons with fully unknown parameters while the designed controller can be only applied to one state of each neuron. These two neurons are connected to each other through synapse. Two different kinds of synapses will be considered in this paper. First, an adaptive controller will be suggested for the case in which the synapse between two neurons is an electrical one. Later, another adaptive controller will be proposed for two neurons connected through chemical synapse. In these two cases the coupling coefficient is considered to be unknown. Proof of asymptotic synchronization of these two neurons will be fully done through using Lyapunov function and finally the effectiveness of proposed controllers will be demonstrated through simulations

Keywords:

Adaptive Synchronization , Hindmarsh-Rose Neuron , Unknown Parameter , Electrical Synapse , Chemical Synapse