Robust Master‐Slave Synchronization of Neuronal Systems

Abstract

The desire to understand physiological mechanisms of neuronal systems has led to the introduction of engineering concepts to explain how the brain works. The synchronization of neurons is a central topic in understanding the behavior of living organisms in neurosciences and has been addressed using concepts from control engineering. We introduce a simple and reliable robust synchronization approach for neuronal systems. The proposed synchronization method is based on a master-slave configuration in conjunction with a coupling input enhanced with compensation of model uncertainties. Our approach has two nice features for the synchronization of neuronal systems: (i) a simple structure that uses the minimum information and (ii) good robustness properties against model uncertainties and noise. Two benchmark neuronal systems, Hodgkin-Huxley and Hindmarsh-Rose neurons, are used to illustrate our findings. The proposed synchronization approach is aimed at gaining insight into the effect of external electrical stimulation of nerve cells.

Unidirectional Synchronization of Hodgkin-Huxley Neurons With Prescribed Performance Under Transcranial Magneto-Acoustical Simulation

“…Compared with the control laws in Octavio Cornejo-Pérez (2005) and Puebla et al (2017), the superior synchronization performance of our adaptive neural controller is obviously revealed. For the sake of fairness, the same master-slaver HH neuron system with the same initial conditions is considered.…”

“…In recent work (Puebla et al, 2017), a simple robust synchronization scheme for HH neural systems was represented by (46) and (47), based on a master-slaver configuration. The detailed parameters can be acquired in Puebla et al (2017).…”

“…Some conclusions for the adaptive hybrid chaotic synchronization of the identical neuron models, using Lyapunov stability theory, were proposed (Aqil et al, 2012; Baladron et al, 2012; Vaidyanathan, 2015). More recently, a novel robust synchronization approach based on the master-slave configuration was introduced for neuronal systems (Puebla et al, 2017), and an adaptive feedback control law was designed for synchronization of the coupled neurons with a time delay (Iqbal et al, 2018). Despite the synchronization control of coupled neurons has been widely investigated, only the steady state synchronization performance has been focused on.…”