Robust neural network control of neural synchronization in the mutually coupled network

Abstract

This paper proposes an adaptive neural network control combined with an input constraint to robustly sustain stable 1 : 1 in-phase synchrony in the presence of unknown deviations in the mutually coupled interneuron (MCI) network parameters. Learning algorithm such as the neural network algorithm (NN) estimates sodium, delayed rectier potassium, and leak channels in a Hodgkin-Huxley model. In addition, the error of 1 : 1 in-phase neural synchrony is ultimately uniformly bounded to zero despite the presence of heterogeneity in the MCI network. The premise on a synchrony problem is that a controller stimulates neurons such that the timing of an impending spike is modulated, but the stimulation itself does not induce action potential spikes. Hence, the saturation function combined with the adaptive controller is employed not to excess input constraint and robustly achieves 1 : 1 synchrony in-phase. Finally, the on-line update law of a NN algorithm is derived from Lyapunov analysis, so that the synchrony stability of uncertain MCI dynamics can be guaranteed.