Adaptive synchronization of two coupled chaotic Hindmarsh–Rose neurons by controlling the membrane potential of a slave neuron

This paper addresses the problem of an adaptive synchronization of two chaotic Hindmarsh–Rose (HR) neurons coupled with a gap junction via a single control input. Two adaptive control approaches (i.e., a nonlinear control when the entire state variables are available and a linear feedback control when only the membrane potential is available) are proposed to guarantee the asymptotic synchronization of the state trajectories of two coupled HR neurons having unknown parameters. Numerical simulations demonstrating and verifying the effectiveness of the proposed control methods are provided.