{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T14:29:45Z","timestamp":1787668185485,"version":"build-2736575974"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2026,7,27]],"date-time":"2026-07-27T00:00:00Z","timestamp":1785110400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,7,27]],"date-time":"2026-07-27T00:00:00Z","timestamp":1785110400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2026,8]]},"DOI":"10.1007\/s12190-026-02863-3","type":"journal-article","created":{"date-parts":[[2026,7,27]],"date-time":"2026-07-27T12:43:59Z","timestamp":1785156239000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Adaptive global polynomial lag synchronization of neural networks with proportional delays"],"prefix":"10.1007","volume":"72","author":[{"given":"Tianyuan","family":"Xu","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"}]},{"given":"Yitong","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,7,27]]},"reference":[{"key":"2863_CR1","doi-asserted-by":"publisher","first-page":"130984","DOI":"10.1016\/j.neucom.2025.130984","volume":"651","author":"Y. Zhang","year":"2025","unstructured":"Zhang, Y., Kou, K.I., Zhang, Y., Liu, L.: Fast fixed-\/preassigned-time synchronization of Clifford-valued neural networks for medical image encryption. Neurocomputing. 651, 130984 (2025). https:\/\/doi.org\/10.1016\/j.neucom.2025.130984","journal-title":"Neurocomputing."},{"issue":"10","key":"2863_CR2","doi-asserted-by":"publisher","first-page":"6424","DOI":"10.1109\/TSMC.2025.3577201","volume":"55","author":"L. Zhou","year":"2025","unstructured":"Zhou, L., Han, J., Zhao, Z., Zhu, Q., Huang, T.: Global polynomial synchronization of proportional delay memristive competitive neural networks with uncertain parameters for image encryption. IEEE Trans. Syst. Man Cybern. Syst. 55(10), 6424\u20136434 (2025). https:\/\/doi.org\/10.1109\/TSMC.2025.3577201","journal-title":"IEEE Trans. Syst. Man, Cybern., Syst."},{"issue":"12","key":"2863_CR3","doi-asserted-by":"publisher","first-page":"1023","DOI":"10.1038\/s43588-023-00558-4","volume":"3","author":"Y. Zhang","year":"2023","unstructured":"Zhang, Y., Yao, Q., Yue, L., Wu, X., Zhang, Z., Lin, Z., Zheng, Y.: Emerging drug interaction prediction enabled by a flow-based graph neural network with biomedical network. Nat. Comput. Sci. 3(12), 1023\u20131033 (2023). https:\/\/doi.org\/10.1038\/s43588-023-00558-4","journal-title":"Nat. Comput. Sci."},{"key":"2863_CR4","doi-asserted-by":"publisher","first-page":"115842","DOI":"10.1016\/j.chaos.2024.115842","volume":"191","author":"G. Chen","year":"2025","unstructured":"Chen, G., Wang, Y., Zhang, X.: New global exponential synchronization conditions for impulsive chaotic neural networks with multiple time-varying leakage and transmission delays: applications for secure communications. Chaos Solitons Fractals 191, 115842 (2025). https:\/\/doi.org\/10.1016\/j.chaos.2024.115842","journal-title":"Chaos, Solitons Fractals"},{"issue":"1","key":"2863_CR5","doi-asserted-by":"publisher","first-page":"37547","DOI":"10.1038\/s41598-025-21462-z","volume":"15","author":"N. Turab","year":"2025","unstructured":"Turab, N., Raghu, N., Choudhury, S., Zkear Abass, A., Roslin, S.E., Kaur, G., Pant, R., Chauhan, G., Khorasanikia Asl, A.: Adaptive sliding mode control for chaotic system synchronization using neural networks. Sci. Rep. 15(1), 37547 (2025). https:\/\/doi.org\/10.1038\/s41598-025-21462-z","journal-title":"Sci. Rep."},{"issue":"8","key":"2863_CR6","doi-asserted-by":"publisher","first-page":"2554","DOI":"10.1073\/pnas.79.8.2554","volume":"79","author":"J.J. Hopfield","year":"1982","unstructured":"Hopfield, J.J.: Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. U.S.A. 79(8), 2554\u20132558 (1982). https:\/\/doi.org\/10.1073\/pnas.79.8.2554","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"issue":"10","key":"2863_CR7","doi-asserted-by":"publisher","first-page":"1257","DOI":"10.1109\/31.7600","volume":"35","author":"L.O. Chua","year":"1988","unstructured":"Chua, L.O., Yang, L.: Cellular neural networks: theory. IEEE Trans. Circuits Syst. 35(10), 1257\u20131272 (1988). https:\/\/doi.org\/10.1109\/31.7600","journal-title":"IEEE Trans. Circuits Syst."},{"issue":"1","key":"2863_CR8","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1103\/PhysRevA.39.347","volume":"39","author":"C.M. Marcus","year":"1989","unstructured":"Marcus, C.M., Westervelt, R.M.: Stability of analog neural networks with delay. Phys. Rev., A 39(1), 347\u2013359 (1989). https:\/\/doi.org\/10.1103\/PhysRevA.39.347","journal-title":"Phys. Rev., A"},{"key":"2863_CR9","doi-asserted-by":"crossref","unstructured":"Roska, T., Chua, L.O.: Cellular neural networks with nonlinear and delay-type template elements. In: IEEE Int. Workshop Cell. Neural Netw. Appl, pp. 12\u201325. IEEE, Budapest, Hungary (1990)","DOI":"10.1109\/CNNA.1990.207503"},{"issue":"8","key":"2863_CR10","doi-asserted-by":"publisher","first-page":"821","DOI":"10.1103\/PhysRevLett.64.821","volume":"64","author":"L.M. Pecora","year":"1990","unstructured":"Pecora, L.M., Carroll T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64(8), 821\u2013824 (1990). https:\/\/doi.org\/10.1103\/PhysRevLett.64.821","journal-title":"Phys. Rev. Lett."},{"issue":"1","key":"2863_CR11","doi-asserted-by":"publisher","first-page":"941426","DOI":"10.1155\/2011\/941426","volume":"2011","author":"L. Zhou","year":"2011","unstructured":"Zhou, L.: On the global dissipativity of a class of cellular neural networks with multipantograph delays. Adv. Artif. Neural Syst. 2011(1), 941426 (2011). https:\/\/doi.org\/10.1155\/2011\/941426","journal-title":"Adv. Artif. Neural Syst."},{"key":"2863_CR12","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/j.neucom.2018.09.030","volume":"321","author":"N. Li","year":"2018","unstructured":"Li, N., Cao, J.: Global dissipativity analysis of quaternion-valued memristor-based neural networks with proportional delay. Neurocomputing 321, 103\u2013113 (2018). https:\/\/doi.org\/10.1016\/j.neucom.2018.09.030","journal-title":"Neurocomputing"},{"issue":"1","key":"2863_CR13","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/s11071-014-1271-y","volume":"77","author":"L. Zhou","year":"2014","unstructured":"Zhou, L.: Global asymptotic stability of cellular neural networks with proportional delays. Nonlinear Dyn. 77(1), 41\u201347 (2014). https:\/\/doi.org\/10.1007\/s11071-014-1271-y","journal-title":"Nonlinear Dyn."},{"issue":"1","key":"2863_CR14","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1109\/TNNLS.2016.2614998","volume":"29","author":"D.T. Son","year":"2018","unstructured":"Son, D.T., Trinh, H., Van Hien, L.: On global dissipativity of nonautonomous neural networks with multiple proportional delays. IEEE Trans. Neural Netw. Learn. Syst. 29(1), 225\u2013231 (2018)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"5","key":"2863_CR15","doi-asserted-by":"publisher","first-page":"4353","DOI":"10.1007\/s12190-024-02136-x","volume":"70","author":"T. Wang","year":"2024","unstructured":"Wang, T., Hu, J., Li, Y., Zhang, G.: Fixed\/preassigned-time synchronization of fuzzy inertial neural networks via event-triggered controller. J. Appl. Math. Comput. 70(5), 4353\u20134371 (2024)","journal-title":"J. Appl. Math. Comput."},{"key":"2863_CR16","doi-asserted-by":"publisher","first-page":"133464","DOI":"10.1016\/j.neucom.2026.133464","volume":"682","author":"G. Zhang","year":"2026","unstructured":"Zhang, G., Hu, J., Wen, S.: New results on fixed\/preassigned-time stabilization of the discontinuous neural networks with mixed time-varying delays. Neurocomputing 682, 133464 (2026). https:\/\/doi.org\/10.1016\/j.neucom.2026.133464","journal-title":"Neurocomputing"},{"key":"2863_CR17","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1016\/j.neucom.2019.09.046","volume":"372","author":"L. Zhou","year":"2020","unstructured":"Zhou, L., Zhao, Z.: Exponential synchronization and polynomial synchronization of recurrent neural networks with and without proportional delays. Neurocomputing 372, 109\u2013116 (2020). https:\/\/doi.org\/10.1016\/j.neucom.2019.09.046","journal-title":"Neurocomputing"},{"key":"2863_CR18","doi-asserted-by":"publisher","first-page":"107889","DOI":"10.1016\/j.neunet.2025.107889","volume":"192","author":"L. Zhou","year":"2025","unstructured":"Zhou, L., Zhang, Y., Yang, X., Han, J.: Global polynomial synchronization of neural networks with bidirectional proportional delays via adaptive pinning control and its application in image encryption. Neural. Networks 192, 107889 (2025). https:\/\/doi.org\/10.1016\/j.neunet.2025.107889","journal-title":"Neural. Networks"},{"key":"2863_CR19","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1016\/j.matcom.2023.01.011","volume":"207","author":"L.-Y. Sun","year":"2023","unstructured":"Sun, L.-Y., Lei, S.-L., Sun, H.-W., Zhang, J.-L.: An $$\\alpha$$-robust fast algorithm for distributed-order time\u2013space fractional diffusion equation with weakly singular solution. Math. Comput. Simul. 207, 437\u2013452 (2023)","journal-title":"Math. Comput. Simul."},{"key":"2863_CR20","doi-asserted-by":"publisher","first-page":"108820","DOI":"10.1016\/j.cnsns.2025.108820","volume":"147","author":"D. Yang","year":"2025","unstructured":"Yang, D., Wang, H., Ren, G., Yu, Y., Zhang, X.-L.: Exponential bipartite synchronization of distributed-order multilayer neural networks with antagonistic interactions via aperiodic intermittent control. Commun. Nonlinear Sci. Numer. Simul. 147, 108820 (2025). https:\/\/doi.org\/10.1016\/j.cnsns.2025.108820","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"issue":"8","key":"2863_CR21","doi-asserted-by":"publisher","first-page":"6383","DOI":"10.1007\/s00521-024-10820-z","volume":"37","author":"V. Kumar","year":"2025","unstructured":"Kumar, V., Heiland, J., Benner, P.: Exponential synchronization of bi-directional associative memory neural networks with delay on arbitrary time domains. Neural Comput. Appl. 37(8), 6383\u20136400 (2025). https:\/\/doi.org\/10.1007\/s00521-024-10820-z","journal-title":"Neural Comput. Appl."},{"key":"2863_CR22","doi-asserted-by":"publisher","first-page":"113150","DOI":"10.1016\/j.chaos.2023.113150","volume":"168","author":"Q. Peng","year":"2023","unstructured":"Peng, Q., Jian, J.: Asymptotic synchronization of second-fractional-order fuzzy neural networks with impulsive effects. Chaos Solitons Fractals 168, 113150 (2023). https:\/\/doi.org\/10.1016\/j.chaos.2023.113150","journal-title":"Chaos, Solitons Fractals"},{"issue":"1","key":"2863_CR23","doi-asserted-by":"publisher","first-page":"783","DOI":"10.1109\/TNNLS.2022.3177234","volume":"35","author":"M. Li","year":"2024","unstructured":"Li, M., Yang, X., Li, X.: Delayed impulsive control for lag synchronization of delayed neural networks involving partial unmeasurable states. IEEE Trans. Neural Netw. Learn. Syst. 35(1), 783\u2013791 (2024). https:\/\/doi.org\/10.1109\/TNNLS.2022.3177234","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"4","key":"2863_CR24","first-page":"414","volume":"40","author":"P. Pei","year":"2023","unstructured":"Pei, P., Han, S., Bian, J., Huang, D., Xue, T.: Lag synchronization analysis of neural networks with generalized delay. J. Xinjiang Univ. Nat. Sci. Ed. 40(4), 414\u2013421,432 (2023)","journal-title":"J. Xinjiang Univ. Nat. Sci. Ed."},{"key":"2863_CR25","doi-asserted-by":"publisher","first-page":"428","DOI":"10.1016\/j.neucom.2022.08.027","volume":"507","author":"Y. Zhang","year":"2022","unstructured":"Zhang, Y., Zhou, L.: Stabilization and lag synchronization of proportional delayed impulsive complex-valued inertial neural networks. Neurocomputing 507, 428\u2013440 (2022). https:\/\/doi.org\/10.1016\/j.neucom.2022.08.027","journal-title":"Neurocomputing"},{"key":"2863_CR26","doi-asserted-by":"publisher","first-page":"113772","DOI":"10.1016\/j.chaos.2023.113772","volume":"174","author":"X. Cui","year":"2023","unstructured":"Cui, X., Li, H.-L., Zhang, L., Hu, C., Bao, H.: Complete synchronization for discrete-time fractional-order coupled neural networks with time delays. Chaos, Solitons Fractals 174, 113772 (2023). https:\/\/doi.org\/10.1016\/j.chaos.2023.113772","journal-title":"Chaos, Solitons Fractals"},{"key":"2863_CR27","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1016\/j.neunet.2023.02.041","volume":"162","author":"Y. Sheng","year":"2023","unstructured":"Sheng, Y., Gong, H., Zeng, Z.: Global synchronization of complex-valued neural networks with unbounded time-varying delays. Neural. Networks 162, 309\u2013317 (2023). https:\/\/doi.org\/10.1016\/j.neunet.2023.02.041","journal-title":"Neural. Networks"},{"key":"2863_CR28","doi-asserted-by":"publisher","first-page":"107255","DOI":"10.1016\/j.neunet.2025.107255","volume":"186","author":"T. Zhang","year":"2025","unstructured":"Zhang, T., Rao, S., Zhou, J.: Heterogeneous boundary synchronization of time-delayed competitive neural networks with adaptive learning parameter in the space-time discretized frames. Neural. Networks 186, 107255 (2025). https:\/\/doi.org\/10.1016\/j.neunet.2025.107255","journal-title":"Neural. Networks"},{"key":"2863_CR29","doi-asserted-by":"publisher","first-page":"129058","DOI":"10.1016\/j.neucom.2024.129058","volume":"618","author":"Y.-L. Huang","year":"2025","unstructured":"Huang, Y.-L., Li, A.-B.: General decay anti-synchronization of coupled delayed memristive neural networks with constant and time-varying distributed-delay coupling. Neurocomputing 618, 129058 (2025). https:\/\/doi.org\/10.1016\/j.neucom.2024.129058","journal-title":"Neurocomputing"},{"issue":"12","key":"2863_CR30","doi-asserted-by":"publisher","first-page":"1935","DOI":"10.3390\/math13121935","volume":"13","author":"C. Wang","year":"2025","unstructured":"Wang, C., Gong, C., Yue, H., Wang, Y.: Event-triggered anti-synchronization of fuzzy delay-coupled fractional memristor-based discrete-time neural networks. Mathematics 13(12), 1935 (2025). https:\/\/doi.org\/10.3390\/math13121935","journal-title":"Mathematics"},{"key":"2863_CR31","doi-asserted-by":"publisher","first-page":"131666","DOI":"10.1016\/j.neucom.2025.131666","volume":"659","author":"Y. Chen","year":"2026","unstructured":"Chen, Y., Wu, A., Li, Y.: Finite-time anti-synchronization of neural networks with general discrete time-varying delays. Neurocomputing 659, 131666 (2026). https:\/\/doi.org\/10.1016\/j.neucom.2025.131666","journal-title":"Neurocomputing"},{"issue":"4","key":"2863_CR32","doi-asserted-by":"publisher","first-page":"1211","DOI":"10.1109\/TNNLS.2019.2919560","volume":"31","author":"R. Kumar","year":"2020","unstructured":"Kumar, R., Sarkar, S., Das, S., Cao, J.: Projective synchronization of delayed neural networks with mismatched parameters and impulsive effects. IEEE Trans. Neural Netw. Learn. Syst. 31(4), 1211\u20131221 (2020). https:\/\/doi.org\/10.1109\/TNNLS.2019.2919560","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"5","key":"2863_CR33","doi-asserted-by":"publisher","first-page":"301","DOI":"10.3390\/fractalfract8050301","volume":"8","author":"H. Fan","year":"2024","unstructured":"Fan, H., Rao, Y., Shi, K., Wen, H.: Time-varying function matrix projection synchronization of caputo fractional-order uncertain memristive neural networks with multiple delays via mixed open loop feedback control and impulsive control. Fractal Fract. 8(5), 301 (2024). https:\/\/doi.org\/10.3390\/fractalfract8050301","journal-title":"Fractal Fract."},{"key":"2863_CR34","doi-asserted-by":"publisher","first-page":"134437","DOI":"10.1016\/j.physd.2024.134437","volume":"471","author":"H. Zhao","year":"2025","unstructured":"Zhao, H., Liu, A., Zhou, L., Niu, S., Gao, X., Zheng, M., Li, X., Li, L.: Predefined-time modified function projective synchronization of memristor-based multidirectional associative memory neural networks with time-varying delay. Physica D. 471, 134437 (2025). https:\/\/doi.org\/10.1016\/j.physd.2024.134437","journal-title":"Physica D."},{"issue":"2","key":"2863_CR35","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1080\/00207179308923005","volume":"58","author":"C.-C. Liu","year":"1993","unstructured":"Liu, C.-C., Chen, F.-C.: Adaptive control of non-linear continuous-time systems using neural networks\u2013general relative degree and MIMO cases. Int J Control. 58(2), 317\u2013335 (1993)","journal-title":"Int J Control."},{"issue":"1","key":"2863_CR36","doi-asserted-by":"publisher","first-page":"6","DOI":"10.53941\/cssc.2025.100006","volume":"1","author":"Q. Yan","year":"2025","unstructured":"Yan, Q., Han, X., Zhou, L., Zheng, M.: Adaptive synchronization of a category of neural networks with proportional delays. Complex Syst. Stab. Control. 1(1), 6 (2025). https:\/\/doi.org\/10.53941\/cssc.2025.100006","journal-title":"Complex Syst. Stab. Control."},{"issue":"1","key":"2863_CR37","doi-asserted-by":"publisher","first-page":"1056","DOI":"10.1109\/TNNLS.2023.3329138","volume":"36","author":"P. Wan","year":"2025","unstructured":"Wan, P., Zhou, Y., Zeng, Z.: Adaptive drive-response synchronization of timescale-type neural networks with unbounded time-varying delays. IEEE Trans. Neural Netw. Learn. Syst. 36(1), 1056\u20131068 (2025). https:\/\/doi.org\/10.1109\/TNNLS.2023.3329138","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"2863_CR38","doi-asserted-by":"publisher","first-page":"117330","DOI":"10.1016\/j.cam.2025.117330","volume":"482","author":"W. Zheng","year":"2026","unstructured":"Zheng, W., Zhou, L.: Global polynomial synchronization of neutral-type cohen-grossberg neural networks with proportional delays and its application to image encryption. J. Comput. Appl. Math. 482, 117330 (2026)","journal-title":"J. Comput. Appl. Math."},{"issue":"5","key":"2863_CR39","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1007\/s40314-026-03797-z","volume":"45","author":"Y. Zhang","year":"2026","unstructured":"Zhang, Y., Zhou, L.: Novel passivity analysis and global polynomial stabilization of complex-valued memristive neural networks with proportional delays for secure image encryption. Comput. Appl. Math. 45(5), 385 (2026)","journal-title":"Comput. Appl. Math."},{"issue":"3","key":"2863_CR40","doi-asserted-by":"publisher","first-page":"619","DOI":"10.1007\/s11063-014-9377-2","volume":"42","author":"L. Zhou","year":"2015","unstructured":"Zhou, L.: Delay-dependent exponential synchronization of recurrent neural networks with multiple proportional delays. Neural. Process. Lett. 42(3), 619\u2013632 (2015). https:\/\/doi.org\/10.1007\/s11063-014-9377-2","journal-title":"Neural. Process. Lett."},{"issue":"9","key":"2863_CR41","doi-asserted-by":"publisher","first-page":"1512","DOI":"10.3390\/math13091512","volume":"13","author":"E. Cong","year":"2025","unstructured":"Cong, E., Zhang, X., Zhu, L.: Semi-global polynomial synchronization of high-order multiple proportional-delay BAM neural networks. Mathematics 13(9), 1512 (2025). https:\/\/doi.org\/10.3390\/math13091512","journal-title":"Mathematics"},{"issue":"8","key":"2863_CR42","doi-asserted-by":"publisher","first-page":"1689","DOI":"10.1140\/epjs\/s11734-024-01198-z","volume":"234","author":"S. Subramaniam","year":"2025","unstructured":"Subramaniam, S., Mani, P.: Adaptive synchronization of the switching stochastic neural networks with time-dependent delays. Eur. Phys. J. Spec. Top. 234(8), 1689\u20131699 (2025). https:\/\/doi.org\/10.1140\/epjs\/s11734-024-01198-z","journal-title":"Eur Phys J Spec Top."},{"issue":"6","key":"2863_CR43","doi-asserted-by":"publisher","first-page":"2872","DOI":"10.1109\/TCSI.2024.3363881","volume":"71","author":"F. Ren","year":"2024","unstructured":"Ren, F., Wang, X., Li, Y., Chen, Z., Wei, C., Zeng, Z.: Fixed-time stabilization of multi-weighted complex networks via novel adaptive pinning chatter-free control and its applications. IEEE Trans. Circuits Syst. I Regul. Pap. 71(6), 2872\u20132884 (2024). https:\/\/doi.org\/10.1109\/TCSI.2024.3363881","journal-title":"IEEE Trans Circuits Syst I Regul Pap."},{"key":"2863_CR44","doi-asserted-by":"publisher","first-page":"110290","DOI":"10.1016\/j.engappai.2025.110290","volume":"147","author":"Y. Wan","year":"2025","unstructured":"Wan, Y., Zhou, L., Han, J.: Global polynomial synchronization of proportional delay memristive neural networks with uncertain parameters and its application to image encryption. Eng. Appl. Artif. Intell. 147, 110290 (2025). https:\/\/doi.org\/10.1016\/j.engappai.2025.110290","journal-title":"Eng. Appl. Artif. Intell"},{"key":"2863_CR45","doi-asserted-by":"publisher","first-page":"107411","DOI":"10.1016\/j.neunet.2025.107411","volume":"188","author":"J. Han","year":"2025","unstructured":"Han, J., Zhou, L.: Fixed-time synchronization of proportional delay memristive complex-valued competitive neural networks. Neural Netw. 188, 107411 (2025). https:\/\/doi.org\/10.1016\/j.neunet.2025.107411","journal-title":"Neural Netw."},{"issue":"1","key":"2863_CR46","doi-asserted-by":"publisher","first-page":"3884","DOI":"10.1038\/s41598-021-82886-x","volume":"11","author":"M.M. Ibrahim","year":"2021","unstructured":"Ibrahim, M.M., Kamran, M.A., Mannan, M.M.N.: Lag synchronization of coupled time-delayed FitzHugh\u2013Nagumo neural networks via feedback control. Sci. Rep. 11(1), 3884 (2021)","journal-title":"Sci. Rep."},{"key":"2863_CR47","doi-asserted-by":"publisher","first-page":"133180","DOI":"10.1016\/j.neucom.2026.133180","volume":"679","author":"Y. Guo","year":"2026","unstructured":"Guo, Y., Zhou, L.: Synchronization of uncertain complex-valued fuzzy memristive neural networks with proportional delays and heterogeneous switching via adaptive event-triggered intermittent control and application to image decryption. Neurocomputing 679, 133180 (2026). https:\/\/doi.org\/10.1016\/j.neucom.2026.133180","journal-title":"Neurocomputing"},{"issue":"5","key":"2863_CR48","doi-asserted-by":"publisher","first-page":"3325","DOI":"10.1109\/TCYB.2022.3176013","volume":"53","author":"L. Liu","year":"2023","unstructured":"Liu, L., Lei, M., Bao, H.: Event-triggered quantized quasisynchronization of uncertain quaternion-valued chaotic neural networks with time-varying delay for image encryption. IEEE Trans. Cybern. 53(5), 3325\u20133336 (2023). https:\/\/doi.org\/10.1109\/TCYB.2022.3176013","journal-title":"IEEE Trans. Cybern."},{"issue":"12","key":"2863_CR49","doi-asserted-by":"publisher","first-page":"18875","DOI":"10.1007\/s11042-021-10511-0","volume":"80","author":"K. Wang","year":"2021","unstructured":"Wang, K., Wu, X., Wang, H., Wang, H., Kan, H., Kurths, J.: New color image cryptosystem via SHA-512 and hybrid domain. Multimedia Tools Appl. 80(12), 18875\u201318899 (2021)","journal-title":"Multimedia Tools Appl."},{"issue":"12","key":"2863_CR50","doi-asserted-by":"publisher","first-page":"5092","DOI":"10.1109\/TNNLS.2019.2963146","volume":"31","author":"L. Zhang","year":"2020","unstructured":"Zhang, L., Nguang, S.K., Ouyang, D., Yan, S.: Synchronization of delayed neural networks via integral-based event-triggered scheme. IEEE Trans. Neural Netw. Learn. Syst. 31(12), 5092\u20135102 (2020). https:\/\/doi.org\/10.1109\/TNNLS.2019.2963146","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-026-02863-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-026-02863-3","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-026-02863-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T13:57:27Z","timestamp":1787666247000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-026-02863-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,27]]},"references-count":50,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2026,8]]}},"alternative-id":["2863"],"URL":"https:\/\/doi.org\/10.1007\/s12190-026-02863-3","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,27]]},"assertion":[{"value":"2 June 2026","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 July 2026","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 July 2026","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 July 2026","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"No known financial conflicts of interest or personal relationships exist that could have influenced the work described in this article, as declared by the authors.","order":1,"name":"Ethics","label":"Competing interests","group":{"name":"EthicsHeading","label":"Declarations"}}],"article-number":"210"}}