Synchronization Analysis of Multiple FitzHugh-Nagumo Noisy and Nonnoisy Neurobiological Networks

In the biological neural bursting and firing synchronization plays a vital role in all neuronal activities that are utilized for making decisions, executing commands, and sending information by neurons and their complex networks in the biological complexed brain. Understanding how the biological brain functionality comes out from different patterns of neuronal transmission between the large group of neural networks stands as one of the enduring challenges of modern neuroscience. This study investigated a methodology for synchronization of multiple single/dual state gap junctions FitzHugh-Nagumo (FHN) drive and slave networks under the condition of external noise. The theory of control was utilized to propose simple and diverse controllers to examine the synchronization problem of the different single and dual state gap junctions coupled nonnoisy and noisy FHN neurobiological drive and slave networks. Control laws are designed to stabilize the error dynamics without direct cancelation and synchronize all the states of both FHN neurobiological drive and slave networks. Sufficient conditions for achieving synchronization in the multiple single/dual state gap junction FHN noisy and nonnoisy neurobiological drive and slave networks were derived analytically using the theory of Lyapunov stability. Furthermore, the proposed controllers have been verified by using five noisy/nonnoisy FHN neurobiological drive and slave networks through numerical simulations.