Abstract
Synchronization of chaotic neurons under external electrical stimulation (EES) is studied in order to understand information processing in the brain and to improve the methodologies employed in the treatment of cognitive diseases. This paper investigates the dynamics of uncertain coupled chaotic delayed FitzHugh-Nagumo (FHN) neurons under EES for incorporated parametric variations. A global nonlinear control law for synchronization of delayed neurons with known parameters is developed. Based on local and global Lipschitz conditions, knowledge of the bounds on the neuronal states, the Lyapunov-Krasovskii functional, and the L 2 gain reduction, a less conservative local robust nonlinear control law is formulated to address the problem of robust asymptotic synchronization of delayed FHN neurons under parametric uncertainties. The proposed local control law guarantees both robust stability and robust performance and provides the L 2 bound for uncertainty rejection in the synchronization error dynamics. Separate conditions for single-input and multiple-input control schemes for synchronization of a wide class of FHN systems are provided. The results of the proposed techniques are verified through numerical simulations.
Highlights
The neuron is the fundamental unit of the functioning brain [1]
The FitzHugh-Nagumo (FHN) model, which has been applied in other fields as well, is one of the most pertinent neural models utilized in synchronization studies [15,16,17,18]
The dynamics of coupled chaotic delayed FHN neurons with gap junctions under electrical stimulation (EES) recently have been investigated [17, 18], which can be accounted for synchronization studies
Summary
The neuron is the fundamental unit of the functioning brain [1]. Its dynamical investigation, for the purpose of measuring brain activity and understanding how the neural system transmits electrochemical signals to the muscles, is one of the most significant challenges facing brain researchers [2,3,4,5,6,7,8]. We propose a novel local robust control law that guarantees asymptotic convergence of synchronization errors to zero under timedelays and parametric uncertainties. This regional control methodology, which is based on local and global Lipschitz constraints on nonlinear and uncertain components of neuronal dynamics, knowledge of state bounds, and the Lyapunov-Krasovskii (LK) functional, is less conservative in its performance within the desired locality. (iii) A less conservative nonlinear control law for local robust synchronization of delayed FHN neurons under parametric uncertainties is developed that ensures asymptotic convergence of synchronization errors to zero.
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