{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T12:10:49Z","timestamp":1776773449513,"version":"3.51.2"},"reference-count":41,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,21]],"date-time":"2023-08-21T00:00:00Z","timestamp":1692576000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this article, the authors analyzed the nonlinear effects of projective synchronization between coupled memristive neural networks (MNNs) and their applications. Since the complete signal transmission is difficult under parameter mismatch and different projective factors, the delays, which are time-varying, and uncertainties have been taken to realize the projective synchronization of MNNs with multi-links under the nonlinear control method. Through the extended comparison principle and a new approach to dealing with the mismatched parameters, sufficient criteria have been determined under different types of projective factors and the framework of the Lyapunov\u2013Krasovskii functional (LKF) for projective convergence of the coupled MNNs. Instead of the classical treatment for secure communication, the concept of error of synchronization between the drive and response systems has been applied to solve the signal encryption\/decryption problem. Finally, the simulations in numerical form have been demonstrated graphically to confirm the adaptability of the theoretical results.<\/jats:p>","DOI":"10.3390\/e25081241","type":"journal-article","created":{"date-parts":[[2023,8,22]],"date-time":"2023-08-22T00:46:22Z","timestamp":1692665182000},"page":"1241","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Projective Synchronization of Delayed Uncertain Coupled Memristive Neural Networks and Their Application"],"prefix":"10.3390","volume":"25","author":[{"given":"Zhen","family":"Han","sequence":"first","affiliation":[{"name":"School of Cybersecurity, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Naipeng","family":"Chen","sequence":"additional","affiliation":[{"name":"International School, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaofeng","family":"Wei","sequence":"additional","affiliation":[{"name":"The 20th Research Institute of China Electronics Technology Group Corporation, Xi\u2019an 710068, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Manman","family":"Yuan","sequence":"additional","affiliation":[{"name":"School of Computer Science, Inner Mongolia University, Hohhot 010021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1000-717X","authenticated-orcid":false,"given":"Huijia","family":"Li","sequence":"additional","affiliation":[{"name":"School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6521","DOI":"10.1007\/s00521-021-06768-z","article-title":"Chaos synchronization using adaptive quantum neural networks and its application in secure communication and cryptography","volume":"34","author":"Aliabadi","year":"2022","journal-title":"Neural Comput. 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