Projective Synchronization of Fractional‐Order BAM Clifford‐Valued Delayed Memristive Neural Networks: An Inner Product‐Based Inequality

ABSTRACT This article is devoted to solving the global Mittag‐Leffler (GML) projective synchronization problem of a new type of fractional‐order BAM memristive Clifford‐valued delayed neural networks (FOBAMMCLVDNNs) using novel inner product‐based inequalities. Unlike existing studies that are based on decomposition methods, we establish novel inner product‐based inequalities using the sign function and the norm of Clifford numbers, allowing us to analyze the dynamics of FOBAMMCLVDNNs without decomposing them into real‐valued systems. Through the established inequalities, the lexicographical order method, and the construction of two new general Lyapunov functions, we obtain some new criteria for the GML projective synchronization problem of FOBAMMCLVDNNs. The derived results include GML complete synchronization and GML anti‐synchronization of FOBAMMCLVDNNs as special cases. To validate the effectiveness of the proposed synchronization criteria, numerical simulations for different cases are presented, accompanied by graphical analysis. Additionally, the obtained results are utilized to develop an image encryption algorithm, and the experimental results verify the proposed encryption algorithm's efficiency for secure communication applications.