{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T13:12:52Z","timestamp":1774098772925,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,19]],"date-time":"2025-02-19T00:00:00Z","timestamp":1739923200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Northeast Forestry University College Student Innovation and Entrepreneurship Training Program Project","award":["DCLXY-2025017"],"award-info":[{"award-number":["DCLXY-2025017"]}]},{"name":"Northeast Forestry University College Student Innovation and Entrepreneurship Training Program Project","award":["LH2022A002"],"award-info":[{"award-number":["LH2022A002"]}]},{"name":"Northeast Forestry University College Student Innovation and Entrepreneurship Training Program Project","award":["12371160"],"award-info":[{"award-number":["12371160"]}]},{"name":"Natural Science Foundation of Heilongjiang Province","award":["DCLXY-2025017"],"award-info":[{"award-number":["DCLXY-2025017"]}]},{"name":"Natural Science Foundation of Heilongjiang Province","award":["LH2022A002"],"award-info":[{"award-number":["LH2022A002"]}]},{"name":"Natural Science Foundation of Heilongjiang Province","award":["12371160"],"award-info":[{"award-number":["12371160"]}]},{"name":"National Natural Science Foundation of China","award":["DCLXY-2025017"],"award-info":[{"award-number":["DCLXY-2025017"]}]},{"name":"National Natural Science Foundation of China","award":["LH2022A002"],"award-info":[{"award-number":["LH2022A002"]}]},{"name":"National Natural Science Foundation of China","award":["12371160"],"award-info":[{"award-number":["12371160"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we consider the pth moment exponential synchronization (PMES) of fuzzy stochastic cellular neural networks (FSCNNs) with discrete and infinite delays. In order to achieve pth-moment exponential synchronization of FSCNNs with discrete and infinite delays, we design an appropriate feedback controller. Using the Lyapunov function method and theories of infinite delayed systems, we obtain some sufficient conditions to ensure the pth-moment exponential synchronization of the system. Finally, to verify the effectiveness of our results, we provide a numerical simulation example. Our results extend the pth-moment exponential synchronization of FSCNNs from finite delays systems to infinite delays systems.<\/jats:p>","DOI":"10.3390\/axioms14020142","type":"journal-article","created":{"date-parts":[[2025,2,19]],"date-time":"2025-02-19T05:34:26Z","timestamp":1739943266000},"page":"142","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["pth Moment Exponential Synchronization of Fuzzy Stochastic Cellular Neural Networks with Discrete and Infinite Delays"],"prefix":"10.3390","volume":"14","author":[{"given":"Keyu","family":"Xu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Northeast Forestry University, Harbin 150040, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1861-1315","authenticated-orcid":false,"given":"Ming","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Northeast Forestry University, Harbin 150040, China"}]},{"given":"Xiaofeng","family":"Xu","sequence":"additional","affiliation":[{"name":"Engineering Research Center of Agricultural Microbiology Technology, Ministry of Education, Harbin 150080, China"},{"name":"Heilongjiang Provincial Key Laboratory of Ecological Restoration and Resource Utilization for Cold Region, Harbin 150080, China"},{"name":"School of Mathematical Science, Heilongjiang University, Harbin 150080, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/S0893-6080(01)00017-X","article-title":"Neural networks for improved target differentiation and localization with sonar","volume":"14","author":"Ayrulu","year":"2001","journal-title":"Neural Netw."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2024","DOI":"10.1080\/00207160.2018.1553297","article-title":"Analysis of associative memories based on cellular neural networks with value-varying templates","volume":"96","author":"Han","year":"2019","journal-title":"Int. J. Comput. Math."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"105839","DOI":"10.1016\/j.sysconle.2024.105839","article-title":"The Stochastic fixed-time synchronization of delays neural networks driven by l\u00e9vy noise","volume":"190","author":"Li","year":"2024","journal-title":"Syst. Control Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1299","DOI":"10.1016\/j.chaos.2009.03.024","article-title":"Synchronization of cellular neural networks of neutral type via dynamic feedback controller","volume":"42","author":"Park","year":"2009","journal-title":"Chaos Soliton Fract."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1430","DOI":"10.1007\/s12555-022-0917-7","article-title":"H\u221e exponential synchronization of switched cellular neural networks based on disturbance observer-based control","volume":"22","author":"Hou","year":"2024","journal-title":"Int. J. Control Autom. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"6047","DOI":"10.3934\/dcdsb.2021001","article-title":"Feedback synchronization of FHN cellular neural networks","volume":"26","author":"Skrzypek","year":"2021","journal-title":"Discret. Contin. Dyn. Syst.-Ser. B"},{"key":"ref_7","unstructured":"Yang, T., Yang, L.B., Wu, C.W., and Chua, L.O. (1996, January 24\u201326). Fuzzy cellular neural networks: Applications. Proceedings of the 1996 Fourth IEEE International Workshop on Cellular Neural Networks and their Applications Proceedings (CNNA-96), Seville, Spain."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.fss.2015.07.009","article-title":"Finite-time synchronization for fuzzy cellular neural networks with time-varying delays","volume":"297","author":"Abdurahman","year":"2016","journal-title":"Fuzzy Sets Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"103106","DOI":"10.1063\/1.5006194","article-title":"Synchronization of fractional fuzzy cellular neural networks with interactions","volume":"27","author":"Ma","year":"2017","journal-title":"Chaos: Interdiscip. J. Nonlinear Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1016\/j.matcom.2011.11.006","article-title":"Exponential lag synchronization for delayed fuzzy cellular neural networks via periodically intermittent control","volume":"82","author":"Yu","year":"2012","journal-title":"Math. Comput. Simul."},{"key":"ref_11","unstructured":"Roska, T., and Chua, L.O. (1990, January 16\u201319). Cellular neural networks with nonlinear and delay-type template elements. Proceedings of the IEEE International Workshop on Cellular Neural Networks and their Applications, Budapest, Hungary."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4674","DOI":"10.1016\/j.physleta.2008.04.053","article-title":"Synchronization of delayed fuzzy cellular neural networks based on adaptive control","volume":"372","author":"Ding","year":"2008","journal-title":"Phys. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1016\/j.neucom.2007.12.005","article-title":"Stability analysis of stochastic fuzzy cellular neural networks with delays","volume":"72","author":"Chen","year":"2008","journal-title":"Neurocomputing"},{"key":"ref_14","first-page":"851","article-title":"Existence and stability of periodic solutions for stochastic fuzzy cellular neural networks with time-varying delay on time scales","volume":"27","author":"Zhang","year":"2018","journal-title":"Dyn. Syst. Appl."},{"key":"ref_15","first-page":"13","article-title":"Adaptive control design for fixed-time synchronization of fuzzy stochastic cellular neural networks with discrete and distributed delay","volume":"18","author":"Liu","year":"2021","journal-title":"Iran. J. Fuzzy Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.fss.2020.07.015","article-title":"Finite-time synchronization of multi-coupling stochastic fuzzy neural networks with mixed delays via feedback control","volume":"411","author":"Xu","year":"2021","journal-title":"Fuzzy Sets Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3244","DOI":"10.1007\/s00034-020-01631-3","article-title":"Finite-time synchronization of fuzzy cellular neural networks with stochastic perturbations and mixed delays","volume":"40","author":"Xu","year":"2021","journal-title":"Circuits Syst. Signal Process."},{"key":"ref_18","first-page":"680","article-title":"Global asymptotic stability of stochastic recurrent neural networks with multiple discrete delays and unbounded distributed delays","volume":"204","author":"Rakkiyappan","year":"2008","journal-title":"Appl. Math. Comput."},{"key":"ref_19","first-page":"1","article-title":"Global exponential stability of fuzzy cellular neural networks with impulses and infinite delays","volume":"28","author":"Wei","year":"2008","journal-title":"J. Math. Res. Expo."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2246","DOI":"10.1016\/j.aml.2012.06.011","article-title":"Global stability for discrete cohen\u2013grossberg neural networks with finite and infinite delays","volume":"25","author":"Li","year":"2012","journal-title":"Appl. Math. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2455","DOI":"10.1016\/j.neucom.2008.11.010","article-title":"Boundedness, periodic solutions and global stability for cellular neural networks with variable coefficients and infinite delays","volume":"72","author":"Jiang","year":"2009","journal-title":"Neurocomputing"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.neunet.2021.05.022","article-title":"Synchronization of recurrent neural networks with unbounded delays and time-varying coefficients via generalized differential inequalities","volume":"143","author":"Zhang","year":"2021","journal-title":"Neural Netw."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1174","DOI":"10.1080\/00207721.2020.1753128","article-title":"Exponential synchronisation of linearly coupled reaction-diffusion neural networks with discrete and infinite distributed delays","volume":"51","author":"He","year":"2020","journal-title":"Int. J. Syst. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/j.cam.2009.12.033","article-title":"Stability analysis of stochastic functional differential equations with infinite delay and its application to recurrent neural networks","volume":"234","author":"Li","year":"2010","journal-title":"J. Comput. Appl. Math."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1335184","DOI":"10.1155\/2023\/1335184","article-title":"The pth moment exponential synchronization of drive-response memristor neural networks subject to stochastic perturbations","volume":"2023","author":"Wang","year":"2023","journal-title":"Complexity"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1007\/s11071-011-0029-z","article-title":"pth moment exponential synchronization for stochastic delayed cohen\u2013grossberg neural networks with markovian switching","volume":"67","author":"Zhu","year":"2011","journal-title":"Nonlinear Dyn."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1016\/j.cam.2007.11.002","article-title":"Stability of stochastic partial differential equations with infinite delays","volume":"222","author":"Luo","year":"2008","journal-title":"J. Comput. Appl. Math."},{"key":"ref_28","unstructured":"Mao, X.R. (1997). Stochastic Differential Equations and Applications, Horwood."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Beckenbach, E., and Bellman, R. (1961). Inequalities, Springer.","DOI":"10.1007\/978-3-642-64971-4"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/2\/142\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:37:34Z","timestamp":1760027854000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/2\/142"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,19]]},"references-count":29,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,2]]}},"alternative-id":["axioms14020142"],"URL":"https:\/\/doi.org\/10.3390\/axioms14020142","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,19]]}}}