{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,13]],"date-time":"2026-08-13T00:27:09Z","timestamp":1786580829454,"version":"build-2736575974"},"reference-count":51,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Communications in Nonlinear Science and Numerical Simulation"],"published-print":{"date-parts":[[2026,11]]},"DOI":"10.1016\/j.cnsns.2026.110576","type":"journal-article","created":{"date-parts":[[2026,7,20]],"date-time":"2026-07-20T07:58:10Z","timestamp":1784534290000},"page":"110576","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"P2","title":["Global exponential synchronization of heterogeneous coupled neural networks with fuzzy-dependent-switching and probabilistic proportional delays"],"prefix":"10.1016","volume":"163","author":[{"given":"Kuo","family":"Yan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2002-0354","authenticated-orcid":false,"given":"Liqun","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.cnsns.2026.110576_bib0001","first-page":"57","article-title":"Advanced applications of neural networks and artificial intelligence: a review","volume":"4","author":"Kumar","year":"2012","journal-title":"J Inf Technol Comput Sci"},{"key":"10.1016\/j.cnsns.2026.110576_bib0002","doi-asserted-by":"crossref","DOI":"10.1016\/j.inffus.2024.102616","article-title":"Data-driven stock forecasting models based on neural networks: a review","volume":"113","author":"Bao","year":"2025","journal-title":"Inf Fusion"},{"key":"10.1016\/j.cnsns.2026.110576_bib0003","doi-asserted-by":"crossref","DOI":"10.1016\/j.cnsns.2025.109511","article-title":"Fault-tolerant impulsive synchronization in hypercomplex neural networks via ai-driven adaptive switching mechanism","volume":"153","author":"Chen","year":"2026","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"10.1016\/j.cnsns.2026.110576_bib0004","doi-asserted-by":"crossref","DOI":"10.1016\/j.cnsns.2025.109479","article-title":"A fixed-time convergence robust zeroing neural network for the synchronization of memristor-based chaotic systems","volume":"152","author":"Fang","year":"2026","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"10.1016\/j.cnsns.2026.110576_bib0005","doi-asserted-by":"crossref","DOI":"10.1016\/j.aml.2021.107709","article-title":"Exponential euler scheme of multi-delay caputo\u2013fabrizio fractional-order differential equations","volume":"124","author":"Zhang","year":"2022","journal-title":"Appl Math Lett"},{"issue":"7","key":"10.1016\/j.cnsns.2026.110576_bib0006","doi-asserted-by":"crossref","first-page":"3379","DOI":"10.1109\/TCYB.2025.3556103","article-title":"Fixed\/prescribed-time synchronization and energy consumption for kuramoto-oscillator networks","volume":"55","author":"Ma","year":"2025","journal-title":"IEEE Trans Cybern"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110576_bib0007","first-page":"697","article-title":"Pth moment exponential synchronization for delayed multi-agent systems with L\u00e9vy noise and Markov switching","volume":"71","author":"Shi","year":"2024","journal-title":"IEEE Trans Circuits Syst II-Express Br"},{"issue":"6","key":"10.1016\/j.cnsns.2026.110576_bib0008","first-page":"2176","article-title":"Finite-time synchronization and energy consumption prediction for multilayer fractional-order networks","volume":"70","author":"Tong","year":"2023","journal-title":"IEEE Trans Circuits Syst II-Express Br"},{"key":"10.1016\/j.cnsns.2026.110576_bib0009","doi-asserted-by":"crossref","DOI":"10.1016\/j.apm.2024.115898","article-title":"Design of double-coupled HR-FN neural network with memristors and its application in image encryption","volume":"140","author":"Wang","year":"2025","journal-title":"Appl Math Modell"},{"issue":"11","key":"10.1016\/j.cnsns.2026.110576_bib0010","doi-asserted-by":"crossref","first-page":"13715","DOI":"10.1007\/s11071-024-10839-w","article-title":"Coexistence and control of firing patterns in a heterogeneous neuron-coupled network by memristive synapses","volume":"113","author":"Wu","year":"2025","journal-title":"Nonlinear Dyn"},{"issue":"14","key":"10.1016\/j.cnsns.2026.110576_bib0011","first-page":"2776","article-title":"Complex dynamical behavior of locally active discrete memristor-coupled neural networks with synaptic crosstalk: attractor coexistence and reentrant feigenbaum trees","volume":"13","author":"Liu","year":"2024","journal-title":"Electron-Switz"},{"key":"10.1016\/j.cnsns.2026.110576_bib0012","doi-asserted-by":"crossref","DOI":"10.1016\/j.cnsns.2025.109448","article-title":"Adaptive pinning synchronization for discrete-time fractional-order uncertain coupled neural networks with time delays","volume":"152","author":"Cui","year":"2026","journal-title":"Nonlinear Sci Numer Simul"},{"issue":"9","key":"10.1016\/j.cnsns.2026.110576_bib0013","doi-asserted-by":"crossref","first-page":"20010","DOI":"10.3934\/math.2025894","article-title":"Finite-time stochastic synchronization of network systems with intermittent delayed couplings","volume":"10","author":"Zhang","year":"2025","journal-title":"AIMS Math"},{"issue":"5","key":"10.1016\/j.cnsns.2026.110576_bib0014","doi-asserted-by":"crossref","first-page":"5731","DOI":"10.1002\/mma.10632","article-title":"Opinion dynamics of two populations with time-delayed coupling","volume":"48","author":"Cicolani","year":"2025","journal-title":"Math Methods Appl Sci"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110576_bib0015","article-title":"Projection synchronization of multi-link coupled memristive neural networks affected by leakage and transmission delays","volume":"140","author":"Hua","year":"2025","journal-title":"Nonlinear Sci Numer Simul"},{"issue":"8","key":"10.1016\/j.cnsns.2026.110576_bib0016","doi-asserted-by":"crossref","first-page":"4702","DOI":"10.1109\/TCYB.2023.3318987","article-title":"Synchronization of coupled neural networks with constant time-delay using sampled-data information","volume":"54","author":"Liu","year":"2023","journal-title":"IEEE Trans Cybern"},{"key":"10.1016\/j.cnsns.2026.110576_bib0017","doi-asserted-by":"crossref","DOI":"10.1016\/j.neucom.2024.129058","article-title":"General decay anti-synchronization of coupled delayed memristive neural networks with constant and time-varying distributed-delay coupling","volume":"618","author":"Huang","year":"2025","journal-title":"Neurocomputing"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110576_bib0018","doi-asserted-by":"crossref","first-page":"3608","DOI":"10.1109\/TNNLS.2024.3357515","article-title":"Synchronization in coupled neural networks with hybrid delayed impulses: average impulsive delay-gain method","volume":"36","author":"Gao","year":"2024","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"10.1016\/j.cnsns.2026.110576_bib0019","doi-asserted-by":"crossref","DOI":"10.1016\/j.neucom.2025.130093","article-title":"Synchronization of coupled neural networks via saturated impulsive correction involving state-dependent delay","volume":"637","author":"Lu","year":"2025","journal-title":"Neurocomputing"},{"key":"10.1016\/j.cnsns.2026.110576_bib0020","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2024.116426","article-title":"A novel adaptive event-triggered controller for exponential quasi-synchronization and synchronization problems to coupled inertial memristive neural networks with time delays","volume":"460","author":"Jiang","year":"2025","journal-title":"J Comput Appl Math"},{"key":"10.1016\/j.cnsns.2026.110576_bib0021","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.neucom.2014.12.016","article-title":"Exponential lag synchronization for delayed memristive recurrent neural networks","volume":"154","author":"Zhang","year":"2015","journal-title":"Neurocomputing"},{"key":"10.1016\/j.cnsns.2026.110576_bib0022","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":"10.1016\/j.cnsns.2026.110576_bib0023","doi-asserted-by":"crossref","first-page":"10574","DOI":"10.1109\/TASE.2025.3525658","article-title":"Fuzzy-based synchronization control for coupled neural networks under cyber attacks via intelligent impulsive algorithm","volume":"22","author":"Dong","year":"2025","journal-title":"IEEE Trans Autom Sci Eng"},{"issue":"3","key":"10.1016\/j.cnsns.2026.110576_bib0024","article-title":"Adaptive fixed-time control for multiple switched coupled neural networks","volume":"3","author":"Zhao","year":"2024","journal-title":"Int J Netw Dyn Intell"},{"issue":"5","key":"10.1016\/j.cnsns.2026.110576_bib0025","doi-asserted-by":"crossref","first-page":"2993","DOI":"10.1109\/TFUZZ.2018.2799171","article-title":"Fault estimation and fault-tolerant control for switched fuzzy stochastic systems","volume":"26","author":"Han","year":"2018","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"7","key":"10.1016\/j.cnsns.2026.110576_bib0026","first-page":"1219","article-title":"Passivity and passification for switched T\u2013S fuzzy systems with sampled-data implementation","volume":"28","author":"Sang","year":"2019","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"10.1016\/j.cnsns.2026.110576_bib0027","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/j.fss.2019.09.001","article-title":"Non-fragile memory filtering of TS fuzzy delayed neural networks based on switched fuzzy sampled-data control","volume":"394","author":"Shi","year":"2020","journal-title":"Fuzzy Sets Syst"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110576_bib0028","doi-asserted-by":"crossref","DOI":"10.1016\/j.jfranklin.2024.107452","article-title":"Reduced-order observer based fault estimation and dynamic output feedback fault-tolerant control for switched fuzzy stochastic systems","volume":"362","author":"Zhang","year":"2025","journal-title":"J Frankl Inst"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110576_bib0029","article-title":"On the global dissipativity of a class of cellular neural networks with multipantograph delays","volume":"2011","author":"Zhou","year":"2011","journal-title":"Adv Art Neural Syst"},{"key":"10.1016\/j.cnsns.2026.110576_bib0030","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.neucom.2019.09.046","article-title":"Exponential synchronization and polynomial synchronization of recurrent neural networks with and without proportional delays","volume":"372","author":"Zhou","year":"2020","journal-title":"Neurocomputing"},{"key":"10.1016\/j.cnsns.2026.110576_bib0031","doi-asserted-by":"crossref","DOI":"10.1016\/j.cnsns.2023.107295","article-title":"Global asymptotic synchronization of inertial memristive Cohen\u2013Grossberg neural networks with proportional delays","volume":"123","author":"Li","year":"2023","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"10.1016\/j.cnsns.2026.110576_bib0032","doi-asserted-by":"crossref","DOI":"10.1016\/j.ins.2024.121150","article-title":"State estimation for proportional delayed complex-valued memristive neural networks","volume":"680","author":"Zhang","year":"2024","journal-title":"Inf Sci"},{"key":"10.1016\/j.cnsns.2026.110576_bib0033","doi-asserted-by":"crossref","DOI":"10.1016\/j.ins.2025.122778","article-title":"Adaptive pinning controller for global polynomial synchronization of inertial memristive neural networks with proportional delays and parameter fluctuations for image encryption","volume":"728","author":"Zheng","year":"2026","journal-title":"Inf Sci"},{"key":"10.1016\/j.cnsns.2026.110576_bib0034","doi-asserted-by":"crossref","first-page":"35255","DOI":"10.1007\/s11071-025-11821-w","article-title":"Adaptive synchronization of memristive complex-valued neural networks with proportional delays and its application to image encryption","volume":"113","author":"Zhou","year":"2025","journal-title":"Nonlinear Dyn"},{"key":"10.1016\/j.cnsns.2026.110576_bib0035","doi-asserted-by":"crossref","DOI":"10.1016\/j.ins.2025.122136","article-title":"General decay projection synchronization of proportional delay memristive competitive neural networks with uncertain parameters for image encryption","volume":"712","author":"Wang","year":"2025","journal-title":"Inf Sci"},{"issue":"10","key":"10.1016\/j.cnsns.2026.110576_bib0036","doi-asserted-by":"crossref","first-page":"6424","DOI":"10.1109\/TSMC.2025.3577201","article-title":"Global polynomial synchronization of proportional delay memristive competitive neural networks with uncertain parameters for image encryption","volume":"55","author":"Zhou","year":"2025","journal-title":"IEEE Trans Syst Man Cybern: Syst"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110576_bib0037","doi-asserted-by":"crossref","DOI":"10.1142\/S179352452250070X","article-title":"Stability analysis of proportional delayed projection neural network for quadratic programming problem","volume":"16","author":"Song","year":"2023","journal-title":"Int J Biomath"},{"key":"10.1016\/j.cnsns.2026.110576_bib0038","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.neucom.2018.11.020","article-title":"Finite-time and fixed-time synchronization of a class of inertial neural networks with multi-proportional delays and its application to secure communication","volume":"332","author":"Alimi","year":"2019","journal-title":"Neurocomputing"},{"key":"10.1016\/j.cnsns.2026.110576_bib0039","doi-asserted-by":"crossref","DOI":"10.1016\/j.neucom.2024.128612","article-title":"Finite-time synchronization of proportional delay memristive competitive neural networks","volume":"610","author":"Han","year":"2024","journal-title":"Neurocomputing"},{"key":"10.1016\/j.cnsns.2026.110576_bib0040","doi-asserted-by":"crossref","DOI":"10.1016\/j.engappai.2025.110290","article-title":"Global polynomial synchronization of proportional delay memristive neural networks with uncertain parameters and its application to image encryption","volume":"147","author":"Wan","year":"2025","journal-title":"Eng Appl Artif Intel"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110576_bib0041","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1109\/TNNLS.2015.2475737","article-title":"Exponential synchronization of coupled stochastic memristor-based neural networks with time-varying probabilistic delay coupling and impulsive delay","volume":"27","author":"Bao","year":"2015","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"10.1016\/j.cnsns.2026.110576_bib0042","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1002\/acs.3968","article-title":"Robust modified repetitive tracking control design for singular Markovian jump fuzzy systems with probabilistic input delay","volume":"39","author":"Mohanapriya","year":"2025","journal-title":"Int J Adapt Control Signal Process"},{"key":"10.1016\/j.cnsns.2026.110576_bib0043","first-page":"310","article-title":"Delay-distribution-dependent exponential stability criteria for discrete-time recurrent neural networks with stochastic delays","volume":"18","author":"Yue","year":"2008","journal-title":"IEEE Trans Neural Netw"},{"issue":"6","key":"10.1016\/j.cnsns.2026.110576_bib0044","doi-asserted-by":"crossref","first-page":"5811","DOI":"10.1007\/s11071-024-10513-1","article-title":"Dynamics in a memristive neural network with three discrete heterogeneous neurons and its application","volume":"113","author":"Luo","year":"2025","journal-title":"Nonlinear Dyn"},{"key":"10.1016\/j.cnsns.2026.110576_bib0045","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1016\/j.neucom.2016.04.051","article-title":"Master\u2013slave synchronization of heterogeneous dimensional delayed neural networks","volume":"205","author":"Li","year":"2016","journal-title":"Neurocomputing"},{"key":"10.1016\/j.cnsns.2026.110576_bib0046","doi-asserted-by":"crossref","DOI":"10.1016\/j.engappai.2024.109871","article-title":"Exponential heterogeneous anti-synchronization of multi-variable discrete stochastic inertial neural networks with adaptive corrective parameter","volume":"142","author":"Zhang","year":"2025","journal-title":"Eng Appl Artif Intell"},{"issue":"3","key":"10.1016\/j.cnsns.2026.110576_bib0047","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1109\/TFUZZ.2020.3048576","article-title":"Dynamic pinning synchronization of fuzzy-dependent-switched coupled memristive neural networks with mismatched dimensions on time scales","volume":"30","author":"Wang","year":"2020","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"10.1016\/j.cnsns.2026.110576_bib0048","doi-asserted-by":"crossref","first-page":"8779","DOI":"10.1007\/s00034-025-03185-8","article-title":"Finite\/fixed-time synchronization of multidimension-valued memristive neural networks","volume":"44","author":"Chen","year":"2025","journal-title":"Circuits Syst Signal Process"},{"key":"10.1016\/j.cnsns.2026.110576_bib0049","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1007\/s11571-025-10234-0","article-title":"A novel predefined-time projective synchronization strategy for multi-modal memristive neural networks","volume":"19","author":"Zhao","year":"2025","journal-title":"Cogn Neurodyn"},{"issue":"12","key":"10.1016\/j.cnsns.2026.110576_bib0050","doi-asserted-by":"crossref","first-page":"18875","DOI":"10.1007\/s11042-021-10511-0","article-title":"New color image cryptosystem via SHA-512 and hybrid domain","volume":"80","author":"Wang","year":"2021","journal-title":"Multimed Tools Appl"},{"issue":"3","key":"10.1016\/j.cnsns.2026.110576_bib0051","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1007\/s11082-018-1363-x","article-title":"Optical double color image encryption scheme in the Fresnel-based Hartley domain using Arnold transform and chaotic logistic adjusted sine phase masks","volume":"50","author":"Faragallah","year":"2018","journal-title":"Opt Quantum Electron"}],"container-title":["Communications in Nonlinear Science and Numerical Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570426009305?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570426009305?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T23:29:35Z","timestamp":1786577375000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1007570426009305"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,11]]},"references-count":51,"alternative-id":["S1007570426009305"],"URL":"https:\/\/doi.org\/10.1016\/j.cnsns.2026.110576","relation":{},"ISSN":["1007-5704"],"issn-type":[{"value":"1007-5704","type":"print"}],"subject":[],"published":{"date-parts":[[2026,11]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Global exponential synchronization of heterogeneous coupled neural networks with fuzzy-dependent-switching and probabilistic proportional delays","name":"articletitle","label":"Article Title"},{"value":"Communications in Nonlinear Science and Numerical Simulation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cnsns.2026.110576","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"110576"}}