Fixed/Predefined-time synchronization of memristor-based complex-valued BAM neural networks for image protection

Abstract

This paper investigates the fixed-time synchronization and the predefined-time synchronization of memristive complex-valued bidirectional associative memory neural networks (MCVBAMNNs) with leakage time-varying delay. First, the proposed neural networks are regarded as two dynamic real-valued systems. By designing a suitable feedback controller, combined with the Lyapunov method and inequality technology, a more accurate upper bound of stability time estimation is given. Then, a predefined-time stability theorem is proposed, which can easily establish a direct relationship between tuning gain and system stability time. Any predefined time can be set as controller parameters to ensure that the synchronization error converges within the predefined time. Finally, the developed chaotic MCVBAMNNs and predefined-time synchronization technology are applied to image encryption and decryption. The correctness of the theory and the security of the cryptographic system are verified by numerical simulation.

Synchronization of Takagi–Sugeno Fuzzy Time-Delayed Stochastic Bidirectional Associative Memory Neural Networks Driven by Brownian Motion in Pre-Assigned Settling Time

“…In the literature, quite a few interesting results were obtained recently in this direction. For example, the finite-time synchronization problems for BAMNNs were treated systematically in References [34,35], the fixed-time synchronization problems associated with BAMNNs were investigated extensively in [36,37] and the references therein, the pre-assigned-time synchronization problems for BAMNNs were also considered in References [38][39][40][41][42][43][44], and some interesting results related to the synchronizability of BAMNNs were presented in References [45][46][47][48][49]. Chen and Zhang [34] as well as Yang and Zhang [35] obtained some finite-time synchronization results for time-delayed BAMNNs via different approaches.…”

“…Chen, Xiong et al [44] and Liu, Zhao et al [43] obtained preassigned synchronization results for complex-valued BAMNNs via different approaches. Liu, Zhao et al [42] applied the pre-assigned synchronization results of complex-valued BAMNNs to image protection. Wang, Zhao et al [38], Mahemuti and Abdurahman [39], Abdurahman, Abudusaimaiti et al [40], as well as You, Abdurahman et al [41] came up with various methods to treat stochastic BAMNNs for their pre-assigned-time synchronizability.…”