In this paper, we consider the synchronization of chaotic Hindmarsh Rose(HR) neurons via a scalar control input.Chaotic HR neurons coupled with a gap junction are taken into consideration, and an active compensation mechanism-based adaptive control is employed to realize the synchronization of two HR neurons. As such an adaptive control is utilized,an accurate model of the system is of no necessity. Asymptotical synchronization of two HR neurons is guaranteed by theoretical results. Numerical results are also provided to confirm the proposed synchronization approach.
In this paper, the relationship between external current stimulus and chaotic behaviors of a Hindmarsh–Rose(HR)neuron is considered. In order to find out the range of external current stimulus which will produce chaotic behaviors of an HR neuron, the Shil'nikov technique is employed. The Cardano formula is taken to obtain the threshold of the chaotic motion, and series solution to a differential equation is utilized to obtain the homoclinic orbit of HR neurons. This analysis establishes mathematically the value of external current input in generating chaotic motion of HR neurons by the Shil'nikov method. The numerical simulations are performed to support the theoretical results.
