{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T22:23:40Z","timestamp":1775082220894,"version":"3.50.1"},"reference-count":43,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T00:00:00Z","timestamp":1773273600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["62266042"],"award-info":[{"award-number":["62266042"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Outstanding Youth Program of Xinjiang, China","award":["2022D01E10"],"award-info":[{"award-number":["2022D01E10"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper investigates the fixed-time (FXT) and predefined-time (PDT) synchronization of memristive neural networks (MNNs) subject to stochastic disturbances, reaction-diffusion terms, and time delays. First, a new PDT stability criterion is established for stochastic nonlinear systems, which permits a priori assignment of the settling time bound regardless of initial conditions, and offers a more concise form than prior results. Second, by leveraging Green\u2019s formula, integral inequality, and stochastic analysis, some sufficient conditions are derived to guarantee FXT and PDT synchronization of introduced stochastic MNNs with reaction-diffusion terms. Finally, numerical simulations are given to validate the effectiveness of the proposed synchronization scheme.<\/jats:p>","DOI":"10.3390\/axioms15030209","type":"journal-article","created":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T09:23:03Z","timestamp":1773307383000},"page":"209","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Fixed\/Predefined-Time Synchronization for Delayed Memristive Reaction-Diffusion Neural Networks Subject to Stochastic Disturbances"],"prefix":"10.3390","volume":"15","author":[{"given":"Gang","family":"Wang","sequence":"first","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ikram","family":"Mamtimin","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2248-4678","authenticated-orcid":false,"given":"Abdujelil","family":"Abdurahman","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1109\/TCSI.2002.807494","article-title":"Global asymptotic stability of a general class of recurrent neural networks with time-varying delays","volume":"50","author":"Cao","year":"2003","journal-title":"IEEE Trans. Circuits Syst. I Fundam. Theory Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"112769","DOI":"10.1016\/j.chaos.2022.112769","article-title":"Parameter estimation of uncertain differential equation by implementing an optimized artificial neural network","volume":"165","author":"Noorani","year":"2022","journal-title":"Chaos Solitons Fractals"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/s12530-025-09681-1","article-title":"Lagrange stability of inertial type neural networks: A Lyapunov Krasovskii functional approach","volume":"16","author":"Maharajan","year":"2025","journal-title":"Evol. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1109\/TCT.1971.1083337","article-title":"Memristor-the missing circuit element","volume":"18","author":"Chua","year":"1971","journal-title":"IEEE Trans. Circuit Theory"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1038\/nature06932","article-title":"The missing memristor found","volume":"453","author":"Strukov","year":"2008","journal-title":"Nature"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"5756","DOI":"10.1109\/TSMC.2024.3408469","article-title":"Quantized Control Based on Stabilization of Discontinuous Memristor-Based Fuzzy Inertial Neural Networks with Proportional Delays","volume":"54","author":"Zhang","year":"2024","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Belmiloudi, A. (2024). Brain Connectivity Dynamics and Mittag-Leffler Synchronization in Asymmetric Complex Networks for a Class of Coupled Nonlinear Fractional-Order Memristive Neural Network System with Coupling Boundary Conditions. Axioms, 13.","DOI":"10.3390\/axioms13070440"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"6651","DOI":"10.1007\/s12190-025-02569-y","article-title":"Fixed-time synchronization of spatiotemporal fuzzy neural network via aperiodic intermittent control with hyperbolic sine function","volume":"71","author":"Abudireman","year":"2025","journal-title":"J. Appl. Math. Comput."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"10123","DOI":"10.1038\/srep10123","article-title":"Electronic system with memristive synapses for pattern recognition","volume":"5","author":"Park","year":"2015","journal-title":"Sci. Rep."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"110316","DOI":"10.1016\/j.chaos.2020.110316","article-title":"New chaotic memristive cellular neural network and its application in secure communication system","volume":"141","author":"Xiu","year":"2020","journal-title":"Chaos Solitons Fractals"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3496","DOI":"10.1007\/s00034-019-01330-8","article-title":"A memristor neural network using synaptic plasticity and its associative memory","volume":"39","author":"Wang","year":"2020","journal-title":"Circuits Syst. Signal Process"},{"key":"ref_12","first-page":"807","article-title":"Bifurcation and control of a predator-prey system with two time delays","volume":"16","author":"Lin","year":"2026","journal-title":"J. Appl. Anal. Comput."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1169","DOI":"10.1140\/epjp\/s13360-022-03302-5","article-title":"Theoretical and numerical results of a stochastic model describing resistance and non-resistance strains of influenza","volume":"137","author":"Farah","year":"2022","journal-title":"Eur. Phys. J. Plus"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"113643","DOI":"10.1016\/j.chaos.2023.113643","article-title":"Fixed\/predefined-time synchronization of coupled memristor-based neural networks with stochastic disturbance","volume":"173","author":"Zhou","year":"2023","journal-title":"Chaos Solitons Fractals"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/TNN.2009.2034318","article-title":"Impulsive control and synchronization for delayed neural networks with reaction-diffusion terms","volume":"21","author":"Hu","year":"2010","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1109\/TNN.2009.2033910","article-title":"Global Asymptotic stability of reaction-diffusion cohen\u2013grossberg neural networks with continuously distributed delays","volume":"21","author":"Wang","year":"2010","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2696","DOI":"10.1109\/TNNLS.2015.2512849","article-title":"Impulsive synchronization of reaction-diffusion neural networks with mixed delays and its application to image encryption","volume":"27","author":"Chen","year":"2016","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2758","DOI":"10.1109\/TCYB.2019.2913200","article-title":"Anti-synchronization in fixed time for discontinuous reaction-diffusion neural networks with time-varying coefficients and time delay","volume":"50","author":"Wang","year":"2020","journal-title":"IEEE Trans. Cybern."},{"key":"ref_19","first-page":"118","article-title":"Adaptive synchronization of memristive neural networks with time-varying delays and reaction-diffusion term","volume":"311","author":"Tu","year":"2017","journal-title":"Appl. Math. Comput."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1109\/TNNLS.2020.2977099","article-title":"Global exponential synchronization of coupled delayed memristive neural networks with reaction-diffusion terms via distributed pinning controls","volume":"32","author":"Guo","year":"2021","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"107539","DOI":"10.1016\/j.knosys.2021.107539","article-title":"Anti-synchronization of delayed memristive neural networks with leakage term and reaction-diffusion terms","volume":"233","author":"Cang","year":"2021","journal-title":"Knowl.-Based Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4658","DOI":"10.1109\/TCYB.2019.2949468","article-title":"Global stabilization of fuzzy memristor-based reaction-diffusion neural networks","volume":"50","author":"Wang","year":"2020","journal-title":"IEEE Trans. Cybern."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1775","DOI":"10.1109\/TFUZZ.2020.2985334","article-title":"Fuzzy adaptive event-triggered sampled-data control for stabilization of T\u2013S fuzzy memristive neural networks with reaction-diffusion terms","volume":"29","author":"Zhang","year":"2021","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.neunet.2022.09.032","article-title":"Pinning synchronization of stochastic neutral memristive neural networks with reaction-diffusion terms","volume":"157","author":"Wu","year":"2023","journal-title":"Neural Netw."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"107673","DOI":"10.1016\/j.cnsns.2023.107673","article-title":"Global exponential stability and stabilization of stochastic memristive neural networks with spatial diffusions and hybrid delays","volume":"128","author":"Shao","year":"2024","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"130537","DOI":"10.1016\/j.neucom.2025.130537","article-title":"Finite-time synchronization of delayed quaternion-valued neural networks by non-decomposition and improved two-step methods","volume":"647","author":"Wang","year":"2025","journal-title":"Neurocomputing"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1109\/TNNLS.2015.2448549","article-title":"A switching approach to designing finite-time synchronization controllers of coupled neural networks","volume":"27","author":"Liu","year":"2016","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2106","DOI":"10.1109\/TAC.2011.2179869","article-title":"Nonlinear feedback design for fixed-time stabilization of linear control systems","volume":"57","author":"Polyakov","year":"2012","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2809","DOI":"10.1007\/s12190-024-02072-w","article-title":"New results on fixed-time synchronization of impulsive neural networks via optimized fixed-time stability","volume":"70","author":"Abdurahman","year":"2024","journal-title":"J. Appl. Math. Comput."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"112202","DOI":"10.1007\/s11432-023-4053-9","article-title":"Aperiodically semi-intermittent-based fixed-time stabilization and synchronization of delayed discontinuous inertial neural networks","volume":"68","author":"Zhang","year":"2025","journal-title":"Sci. China Inf. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"8485","DOI":"10.1109\/TNNLS.2024.3414276","article-title":"Fixed-time passivity and synchronization of multiweighted coupled memristive neural networks with adaptive couplings","volume":"36","author":"Tang","year":"2025","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"52","DOI":"10.62762\/JNDA.2025.841722","article-title":"Semi-Intermittent Control Based Fixed\/Predefined-Time Synchronization of Spatiotemporal Memristive Neural Networks","volume":"1","author":"Qiao","year":"2025","journal-title":"J. Nonlinear Dyn. Appl."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"12085","DOI":"10.1109\/ACCESS.2018.2805183","article-title":"Fixed-time synchronization of memristive fuzzy BAM cellular neural networks with time-varying delays based on feedback controllers","volume":"6","author":"Zheng","year":"2018","journal-title":"IEEE Access"},{"key":"ref_34","first-page":"127671","article-title":"New results on fixed\/predefined-time synchronization of delayed fuzzy inertial discontinuous neural networks: Non-reduced order approach","volume":"440","author":"Zhang","year":"2023","journal-title":"Appl. Math. Comput."},{"key":"ref_35","first-page":"127811","article-title":"Fixed\/predefined-time lag synchronization of complex-valued BAM neural networks with stochastic perturbations","volume":"444","author":"Abdurahman","year":"2023","journal-title":"Appl. Math. Comput."},{"key":"ref_36","first-page":"3644","article-title":"Fixed-Time and Predefined-Time Synchronization of Discontinuous Neutral-Type Competitive Networks via Non-Chattering Adaptive Control Strategy","volume":"10","author":"Kong","year":"2023","journal-title":"IEEE Trans. Netw. Sci. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"111596","DOI":"10.1016\/j.chaos.2021.111596","article-title":"Fixed\/predefined-time synchronization of fuzzy neural networks with stochastic perturbations","volume":"154","author":"Abudusaimaiti","year":"2022","journal-title":"Chaos Solitons Fractals"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2671","DOI":"10.1016\/j.automatica.2011.08.050","article-title":"Finite-time stability and instability of stochastic nonlinear systems","volume":"47","author":"Yin","year":"2011","journal-title":"Automatica"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.automatica.2019.05.048","article-title":"Generalized Lyapunov criteria on finite-time stability of stochastic nonlinear systems","volume":"107","author":"Yu","year":"2019","journal-title":"Automatica"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"5052","DOI":"10.1109\/TAC.2022.3218592","article-title":"Fixed-time Lyapunov criteria of stochastic nonlinear systems and its generalization","volume":"68","author":"Min","year":"2023","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"182202","DOI":"10.1007\/s11432-022-3690-y","article-title":"Predefined-time stabilization for nonlinear stochastic It\u00f4 systems","volume":"66","author":"Zhang","year":"2023","journal-title":"Sci. China Inf. Sci."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/j.chaos.2007.05.002","article-title":"Global exponential stability and periodicity of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions","volume":"35","author":"Lu","year":"2008","journal-title":"Chaos Solitons Fractals"},{"key":"ref_43","unstructured":"Noorizadegan, A., Wang, S.F., Ling, L.V., and Dominguez-Morales, J.P. (2026). A practitioner\u2019s guide to Kolmogorov-Arnold networks. arXiv."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/15\/3\/209\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T05:12:39Z","timestamp":1773465159000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/15\/3\/209"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,12]]},"references-count":43,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2026,3]]}},"alternative-id":["axioms15030209"],"URL":"https:\/\/doi.org\/10.3390\/axioms15030209","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,12]]}}}