Fixed-time adaptive stochastic synchronization for chaotic systems with uncertainties

This paper addresses the fixed-time synchronization problem for a class of uncertain chaotic systems subject to stochastic perturbations. To solve this problem, novel continuous-time fixed-time stability theorems are established for both deterministic and stochastic systems. A key innovation is that the parameters b and c in these theorems can be either positive or negative, overcoming limitations inherent in traditional approaches. Furthermore, leveraging these fixed-time stability theorems and an adaptive control method, a novel sufficient condition for achieving fixed-time stochastic synchronization is proposed. This control scheme is innovative in its simultaneous handling of both model uncertainties and stochastic effects. Finally, the effectiveness and robustness of the proposed approach are demonstrated through numerical simulations on the Lorenz-84 chaotic system, including comparative analysis with existing methods.