Finite/fixed-time synchronization of inertial memristive neural networks by interval matrix method for secure communication.

This paper investigates the finite/fixed-time synchronization problem of delayed inertial memristive neural networks (DIMNNs) using interval matrix-based methods within a unified control framework. By employing set-valued mapping and differential inclusion theory, two distinct methods are applied to handle the switching behavior of memristor parameters: the maximum absolute value method and the interval matrix method. Based on these different approaches, two control strategies are proposed to select appropriate control parameters, enabling the system to achieve finite and fixed-time synchronization, respectively. Additionally, the resulting theoretical criteria differ based on the chosen control strategy, with one expressed in algebraic form and the other in the form of linear matrix inequalities (LMIs). Numerical simulations demonstrate that the interval matrix method outperforms the maximum absolute value method in terms of handling memristor parameter switching, achieving faster finite/fixed-time synchronization. Furthermore, the theoretical results are extended to the field of image encryption, where the response system is utilized for decryption and expanding the keyspace. • Inertial memristive neural networks (IMNNs) employ two methods to manage switching behaviors: maximum absolute value and interval matrix. • Controllers based on these methods yield distinct theorems: one in algebraic form and the other in the form of linear matrix inequalities (LMIs). • Simulation shows Theorem 2 (interval matrix) yields faster synchronization convergence than Theorem 1 (maximum absolute value), and the findings are also applicable to image encryption. [ABSTRACT FROM AUTHOR]