<p>This paper proposes a novel sliding mode control framework featuring a composite multi-power reaching law (CMPRL) and a central cyclic memristive neural network (CCMNN) model. The reaching law combines multiple fractional power terms with a time varying gain schedule to force the sliding variable to zero exactly at a user-prescribed time bound. Unlike conventional reaching laws that rely on discontinuous signum functions or single power-term feedback, the proposed law uniquely integrates linear, fractional-order and superlinear power terms with an adaptive exponential transformation and an arctangent-based saturation term, thereby ensuring exact, predefined-time convergence while producing a smooth, bounded control input. A novel CCMNN model is also formulated, featuring memristive self synapses in a central loop, which endows the network with enhanced memory effects and rich multi-scroll chaotic dynamics. By coupling the CCMNN with the composite reaching law, a sliding-mode controller is obtained that guarantees global predefined-time synchronization of drive-response CCMNN pairs and demonstrates robustness against memristor non-idealities and parameter uncertainties. The predefined-time convergence of the reaching law and the sliding mode synchronization controller is rigorously proved, independent of the initial error. Compared with the existing reaching law methods, our CMPRL has accurate convergence at the design level, has strong chatter suppression capability, and can achieve network synchronization more smoothly. The correctness and universality of the obtained results are verified by numerical simulations.</p>