Analysis of Synchronization of Classes of Delayed Neural Networks under control strategies and Its Application

Abstract

This thesis investigates the synchronization problems of various classes of neural networks (NNs) with time-varying and proportional delays in continuous-time settings, motivated by their wide applications in secure communication and image encryption. The inherent challenges posed by parameter uncertainties, diusion terms, memristive ects, and impulsive delays are systematically addressed through advanced control and stability techniques. First, the synchronization of fuzzy reaction di usion neural networks (FRDNNs) with time-varying transmission delays is studied via aperiodic semi-intermittent hybrid control, introducing the concept of average control width (ACW) alongside average dwell time (ADT). The study further extends to reaction di usion inertial memristive neural networks (RDIMNNs), where global polynomial synchronization (GPS) is achieved by proposing proportional delay-dependent aperiodically intermittent event-triggered impulsive control (API-ETIC) and deriving new delay di erential inequalities (DDIs). Next, global polynomial pinning synchronization (GPPS) of coupled reaction di usion inertial neural networks (CRDINNs) with proportional delays is analyzed under cyber-attack environments, where a novel dual event-triggered Markov-switched control (DETMC) and a proportional-delay Halanay inequality are established. Additionally, synchronization of general time-delay dynamical networks is explored through hybrid delayed impulses with an aperiodically intermittent control scheme, where a dual-sequence framework is proposed together with new Razumikhintype inequalities based on average impulsive interval (AII), average impulsive delay (AID), and average impulsive gain (AIG). Across these contributions, new Lyapunov-based functionals, inequality techniques, and linear matrix inequality (LMI) criteria are developed to derive exible and less conservative synchronization conditions. The theoretical frameworks are rigorously validated with numerical simulations and further extended to practical applications in secure medical image encryption. Novel encryption schemes are designed using chaos-based sequences and improved scrambling di usion strategies such as Arnold cat map, Zigzag, Raster, Knight's tour, corner traversal, and space- lling curves, integrated with elliptic curve cryptography. Extensive statistical and robustness analyses con rm the high security and e ciency of the proposed approaches. Overall, this thesis establishes a uni ed synchronization framework for diverse delayed neural networks under uncertainties, proportional delays, impulses, and cyber attacks, while demonstrating its e ectiveness in advancing modern image security systems.