Multi-switching robust anti-synchronisation of chaotic systems with external disturbances

Synchronisation of multiple chaotic systems in the presence of external disturbances is a challenging problem with significant relevance to secure communication. This article addresses this issue by developing a novel synchronisation framework, termed multiswitching quadratic compound combination anti-synchronisation, for five n-dimensional chaotic systems. The main objective is to enhance the complexity and security of chaotic synchronisation schemes by incorporating multiswitching of signals, thereby strengthening resistance against unauthorised signal interception. The proposed methodology employs the Lorenz, Rössler, and Lü chaotic systems as drive systems, while the Bhalekar–Gejji and Pehlivan chaotic systems are considered as response systems. Nonlinear control laws are designed using Lyapunov stability theory to guarantee convergence of synchronisation errors in the presence of bounded external disturbances. Numerical simulations and graphical MATLAB results confirm the effectiveness and robustness of the proposed scheme. The results demonstrate that the framework offers a flexible and secure approach suitable for advanced secure communication applications.