همگام‌سازي شبكه‌ي نورون‌هاي تاخيردار براساس مدل FHN با استفاده از روش‌‌هاي كنترل غيرخطي

Neurons constitute the fundamental units of the brain’s neural network an‎d enable information processing required for the brain’s vital functions. Neural networks communicate with one another, an‎d through synchronization among them, the brain is able to process information efficiently. Synchronization plays a crucial role in cognitive–motor activities, enhancement of information processing, an‎d maintenance of the nervous system’s balance, highlighting its significance in brain neural networks. Neuronal synchronization is the central focus of this study, with potential applications including the improvement of neural connectivity an‎d the treatment of certain neurological disorders such as autism an‎d attention-deficit/hyperactivity disorder (ADHD). To model neuronal dynamics, the FitzHugh–Nagumo (FHN) model is employed in this research. Initially, a ring-connected neural network in the presence of disturbances is introduced, an‎d its stability is analyzed an‎d proven using linear control. Subsequently, a fully connected neural network is investigated, for which a sliding mode controller is designed an‎d its stability is rigorously established. The performance of the controller in the presence of time delays is then examined by incorporating delays into the network, re-establishing stability, an‎d analyzing their effects through numerical simulations. In the next stage, a brain atlas comprising 90 regions along with a realistic connectivity matrix is considered; a controller is designed for this network an‎d its stability is proven. Thereafter, uncertainties an‎d disturbances are introduced into the system, stability is re-established, an‎d the impacts of uncertainties an‎d disturbances on network performance are investigated The controller performance is eva‎luated by computing quantitative metrics such as synchronization error an‎d mean square error, as well as by analyzing graphical representations including neuronal firing rates. These eva‎luations enable a separate an‎d systematic assessment of the effectiveness of each proposed control strategy.

مرضيه كمالي , احسان روحاني

مريم ذكري , جلال ذهبي