Simple noise reduction in the adaptive synchronization of coupled neurons by Robust Fixed Point Transformation

To avoid the general mathematical difficulties of the application of Lyapunov´s “direct” method in adaptive control in the present paper an alternative approach, the use of “Robust Fixed Point Transformation (RFPT)” is applied for the adaptive synchronization of two coupled, asymmetric, chaotically behaving, approximately known Fitz - Hugh - Nagumo (FHN) neurons. Since the RFPT scheme is based on the use of the “Expected - Realized Response Scheme” the noise in the observed quantities may influence the efficiency of the controller. For this purpose the use of a very simple, easily realizable technique is proposed that applies polynomial filtering coefficients in the time domain. Its efficiency is investigated and substantiated via extended simulation investigations.