Synchronisation of multi-weighted coupled delayed systems with Lévy noise under adaptive intermittent control

This paper investigates the exponential synchronisation of multi-weighted coupled delayed networks with Lévy noise via adaptive aperiodically intermittent control. To overcome the limitations of traditional periodically intermittent control methods, we propose an adaptive aperiodically intermittent control strategy that dynamically adjusts both control gains and intermittent periods, effectively addressing the synchronisation challenges posed by the combined effects of multi-weighted topology, time-varying coupling, and Lévy noise. By employing Lyapunov stability theory and algebraic graph theory, we construct a global Lyapunov function and establish novel criteria for ensuring pth moment exponential synchronisation. The derived conditions explicitly reveal quantitative relationships between control parameters, network topology, and noise intensity. Notably, the proposed adaptive mechanism can dynamically optimise control efficiency according to system characteristics. Finally, numerical simulations of coupled Chua's circuits validate the effectiveness and practicality of theoretical results.