Abstract
Due to its complexity, the problem of predefined-time synchronization in multimodal memristive neural networks has rarely been explored in the literature. This paper is the first to systematically study this issue, filling a research gap in the field and further enriching the related theoretical framework. First, a novel predefined-time stability theorem is proposed, which features more lenient judgment conditions compared to existing methods. This significantly enhances the generality of the stability theorem, making it applicable to a wider range of practical engineering projects. Second, based on the proposed predefined-time stability theorem, as well as the theories of differential inclusion, Filippov solutions, and set-valued mapping, a simple and practical feedback controller is developed. This controller establishes the necessary criteria for achieving predefined-time projective synchronization in multimodal memristive neural networks. Finally, two intricate simulation experiments are carefully designed. These experiments validate the effectiveness and feasibility of the theoretical derivations presented in this paper.