{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T06:07:56Z","timestamp":1757311676700,"version":"3.37.3"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"16","license":[{"start":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T00:00:00Z","timestamp":1648684800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T00:00:00Z","timestamp":1648684800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput & Applic"],"published-print":{"date-parts":[[2022,8]]},"DOI":"10.1007\/s00521-022-07177-6","type":"journal-article","created":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T13:21:23Z","timestamp":1648732883000},"page":"13649-13666","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Stochastic stability for delayed semi-Markovian genetic regulatory networks with partly unknown transition rates by employing new integral inequalities"],"prefix":"10.1007","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1505-8873","authenticated-orcid":false,"given":"Cheng-De","family":"Zheng","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zeda","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Lu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huaguang","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,3,31]]},"reference":[{"key":"7177_CR1","doi-asserted-by":"publisher","first-page":"763","DOI":"10.1016\/j.neucom.2016.05.066","volume":"207","author":"Z Li","year":"2016","unstructured":"Li Z, Chen D, Liu Y, Zhao Y (2016) New delay-dependent stability criteria of genetic regulatory networks subject to variable delays. Neurocomputing 207:763\u2013771","journal-title":"Neurocomputing"},{"key":"7177_CR2","doi-asserted-by":"crossref","unstructured":"Gu K (2000) An integral inequality in the stability problem of time-delay systems. In: Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, pp 2805\u20132810","DOI":"10.1109\/CDC.2000.914233"},{"key":"7177_CR3","doi-asserted-by":"publisher","first-page":"981","DOI":"10.1016\/j.neucom.2016.07.018","volume":"214","author":"S Senthilraj","year":"2016","unstructured":"Senthilraj S, Raja R, Zhu Q, Samidurai R, Zhou H (2016) Delay-dependent asymptotic stability criteria for genetic regulatory networks with impulsive perturbations. Neurocomputing 214:981\u2013990","journal-title":"Neurocomputing"},{"key":"7177_CR4","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1016\/j.neucom.2013.03.046","volume":"119","author":"W Wang","year":"2013","unstructured":"Wang W, Zhong S, Nguang SK, Liu F (2013) Robust delay-probability-distribution-dependent stability of uncertain genetic regulatory networks with variable delays. Neurocomputing 119:153\u2013164","journal-title":"Neurocomputing"},{"issue":"1","key":"7177_CR5","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1016\/j.automatica.2010.10.014","volume":"47","author":"MJ Park","year":"2011","unstructured":"Park MJ, Ko JW, Jeong CK (2011) Reciprocally convex approach to stability of systems with variable delays. Automatica 47(1):235\u2013238","journal-title":"Automatica"},{"issue":"16","key":"7177_CR6","doi-asserted-by":"publisher","first-page":"2574","DOI":"10.1002\/rnc.3011","volume":"24","author":"W Wang","year":"2014","unstructured":"Wang W, Zhong S, Liu F, Cheng J (2014) Robust delay-probability-distribution-dependent stability of uncertain stochastic genetic regulatory networks with random discrete delays and distributed delays. Int J Robust Nonlinear Control 24(16):2574\u20132596","journal-title":"Int J Robust Nonlinear Control"},{"key":"7177_CR7","doi-asserted-by":"publisher","first-page":"94","DOI":"10.1016\/j.mbs.2016.06.004","volume":"278","author":"L Wang","year":"2016","unstructured":"Wang L, Luo Z-P, Yang H-L, Cao J (2016) Stability of genetic regulatory networks based on switched systems and mixed time-delays. Math Biosci 278:94\u201399","journal-title":"Math Biosci"},{"issue":"6","key":"7177_CR8","doi-asserted-by":"publisher","first-page":"1005","DOI":"10.1007\/s13042-014-0306-5","volume":"7","author":"X Zhang","year":"2016","unstructured":"Zhang X, Li R, Han C, Yao R (2016) Robust stability analysis of uncertain genetic regulatory networks with mixed time delays. Int J Mach Learn Cyber 7(6):1005\u20131022","journal-title":"Int J Mach Learn Cyber"},{"issue":"7","key":"7177_CR9","first-page":"3047","volume":"29","author":"T Yu","year":"2018","unstructured":"Yu T, Liu J, Zeng Y, Zhang X, Zeng Q, Wu L (2018) Stability analysis of genetic regulatory networks with switching parameters and time delays. IEEE Trans Neural Netw Learn Syst 29(7):3047\u20133058","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"7177_CR10","doi-asserted-by":"publisher","first-page":"1569","DOI":"10.1016\/j.cnsns.2013.09.008","volume":"19","author":"W Wang","year":"2014","unstructured":"Wang W, Nguang SK, Zhong S, Liu F (2014) Robust stability analysis of stochastic delayed genetic regulatory networks with polytopic uncertainties and linear fractional parametric uncertainties. Commun Nonlinear Sci Numer Simulat 19:1569\u20131581","journal-title":"Commun Nonlinear Sci Numer Simulat"},{"key":"7177_CR11","doi-asserted-by":"publisher","first-page":"1060","DOI":"10.1016\/j.neucom.2015.10.024","volume":"174B","author":"X Zhang","year":"2016","unstructured":"Zhang X, Han Y, Wu L, Zou J (2016) M-matrix-based globally asymptotic stability criteria for genetic regulatory networks with variable discrete and unbounded distributed delays. Neurocomputing 174B:1060\u20131069","journal-title":"Neurocomputing"},{"key":"7177_CR12","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1016\/j.neucom.2016.09.017","volume":"219","author":"J Qiu","year":"2017","unstructured":"Qiu J, Sun K, Yang C, Chen X, Chen X, Zhang A (2017) Finite-time stability of genetic regulatory networks with impulsive effects. Neurocomputing 219:9\u201314","journal-title":"Neurocomputing"},{"key":"7177_CR13","doi-asserted-by":"publisher","first-page":"1225","DOI":"10.1016\/j.neucom.2014.09.005","volume":"149C","author":"L Li","year":"2015","unstructured":"Li L, Yang Y (2015) On sampled-data control for stabilization of genetic regulatory networks with leakage delays. Neurocomputing 149C:1225\u20131231","journal-title":"Neurocomputing"},{"issue":"3","key":"7177_CR14","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1007\/s11071-014-1327-z","volume":"77","author":"H Zhang","year":"2014","unstructured":"Zhang H, Zhao M, Wang Z, Wu Z (2014) Adaptive synchronization of an uncertain coupling complex network with time-delay. Nonlinear Dyn 77(3):643\u2013653","journal-title":"Nonlinear Dyn"},{"issue":"7","key":"7177_CR15","doi-asserted-by":"publisher","first-page":"1229","DOI":"10.1109\/TNNLS.2014.2317880","volume":"25","author":"H Zhang","year":"2014","unstructured":"Zhang H, Wang Z, Liu D (2014) A comprehensive review of stability analysis of continuous-time recurrent neural networks. IEEE Trans Neural Netw Learning Syst 25(7):1229\u20131261","journal-title":"IEEE Trans Neural Netw Learning Syst"},{"key":"7177_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.nahs.2014.04.003","volume":"14","author":"S Lakshmanan","year":"2014","unstructured":"Lakshmanan S, Rihan FA, Rakkiyappan R, Park JH (2014) Stability analysis of the differential genetic regulatory networks model with variable delays and Markovian jumping parameters. Nonlinear Anal Hybrid Syst 14:1\u201315","journal-title":"Nonlinear Anal Hybrid Syst"},{"issue":"7","key":"7177_CR17","doi-asserted-by":"publisher","first-page":"1615","DOI":"10.1016\/j.jfranklin.2016.01.015","volume":"353","author":"K Ratnavelu","year":"2016","unstructured":"Ratnavelu K, Kalpana M, Balasubramaniam P (2016) Asymptotic stability of Markovian switching genetic regulatory networks with leakage and mode-dependent time delays. J Franklin Inst 353(7):1615\u20131638","journal-title":"J Franklin Inst"},{"issue":"11","key":"7177_CR18","doi-asserted-by":"publisher","first-page":"3349","DOI":"10.1007\/s00034-014-9805-6","volume":"33","author":"VM Revathi","year":"2014","unstructured":"Revathi VM, Balasubramaniam P, Ratnavelu K (2014) Mode-dependent H\u221e filtering for stochastic Markovian switching genetic regulatory networks with leakage and variable delays. Circuits Syst Signal Process 33(11):3349\u20133388","journal-title":"Circuits Syst Signal Process"},{"issue":"6","key":"7177_CR19","doi-asserted-by":"publisher","first-page":"2488","DOI":"10.1109\/TNNLS.2017.2696582","volume":"29","author":"Y Wei","year":"2018","unstructured":"Wei Y, Park JH, Karimi HR, Tian Y-C, Jung H (2018) Improved stability and stabilization results for stochastic synchronization of continuous-time semi-Markovian jump neural networks with variable delay. IEEE Trans Neural Netw Learn Syst 29(6):2488\u20132501","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"5","key":"7177_CR20","doi-asserted-by":"publisher","first-page":"2001","DOI":"10.1002\/rnc.4859","volume":"30","author":"H Zhang","year":"2020","unstructured":"Zhang H, Qiu Z, Liu X, Xiong L (2020) Stochastic robust finite-time boundedness for semi-Markov jump uncertain neutral-type neural networks with mixed time-varying delays via a generalized reciprocally convex combination inequality. Int J Robust Nonlinear Control 30(5):2001\u20132019","journal-title":"Int J Robust Nonlinear Control"},{"key":"7177_CR21","doi-asserted-by":"publisher","first-page":"8","DOI":"10.1016\/j.neucom.2012.12.046","volume":"113","author":"X Zhang","year":"2013","unstructured":"Zhang X, Yu A, Zhang G (2013) M-matrix-based delay-range-dependent global asymptotical stability criterion for genetic regulatory networks with time-varying delays. Neurocomputing 113:8\u201315","journal-title":"Neurocomputing"},{"key":"7177_CR22","first-page":"628","volume":"274","author":"T Liu","year":"2016","unstructured":"Liu T, Zhang X, Gao X (2016) Stability analysis for continuous-time and discrete-time genetic regulatory net- works with delays. Appl Math Comput 274:628\u2013643","journal-title":"Appl Math Comput"},{"issue":"3","key":"7177_CR23","doi-asserted-by":"publisher","first-page":"740","DOI":"10.1109\/TNNLS.2015.2507790","volume":"28","author":"H Zhang","year":"2017","unstructured":"Zhang H, Wang J, Wang Z, Liang H (2017) Sampled-data synchronization analysis of Markovian neural net- works with generally incomplete transition rates. IEEE Trans Neural Netw Learning Syst 28(3):740\u2013752","journal-title":"IEEE Trans Neural Netw Learning Syst"},{"issue":"11","key":"7177_CR24","doi-asserted-by":"publisher","first-page":"3384","DOI":"10.1109\/TNNLS.2019.2891552","volume":"30","author":"R Zhang","year":"2019","unstructured":"Zhang R, Zeng D, Liu X, Zhong S, Cheng J (2019) New results on stability analysis for delayed Markovian generalized neural networks with partly unknown transition rates. IEEE Trans Neural Netw Learning Syst 30(11):3384\u20133395","journal-title":"IEEE Trans Neural Netw Learning Syst"},{"issue":"7","key":"7177_CR25","doi-asserted-by":"publisher","first-page":"1660","DOI":"10.1109\/TAC.2011.2121410","volume":"56","author":"C Briat","year":"2011","unstructured":"Briat C (2011) Convergence and equivalence results for the Jensen\u2019s inequality: application to time-delay and sampled-data systems. IEEE Trans Autom Control 56(7):1660\u20131665","journal-title":"IEEE Trans Autom Control"},{"issue":"9","key":"7177_CR26","first-page":"2860","volume":"49","author":"A Seuret","year":"2013","unstructured":"Seuret A, Gouaisbaut F (2013) Wirtinger-based integral inequality: application to time-delay systems. Auto- matica 49(9):2860\u20132866","journal-title":"Auto- matica"},{"key":"7177_CR27","doi-asserted-by":"publisher","first-page":"204","DOI":"10.1016\/j.automatica.2015.03.010","volume":"55","author":"MJ Park","year":"2015","unstructured":"Park MJ, Kwon OM, Park JH, Lee SM, Cha EJ (2015) Stability of time-delay systems via Wirtinger-based double integral inequality. Automatica 55:204\u2013208","journal-title":"Automatica"},{"key":"7177_CR28","doi-asserted-by":"crossref","unstructured":"Seuret A, Gouaisbaut F (2014) Complete quadratic Lyapunov functionals using Bessel\u2013Legendre inequality. In: Proceedings of European Control Conference, Strasbourg, France, pp 448\u2013453","DOI":"10.1109\/ECC.2014.6862453"},{"issue":"4","key":"7177_CR29","doi-asserted-by":"publisher","first-page":"1378","DOI":"10.1016\/j.jfranklin.2015.01.004","volume":"352","author":"PG Park","year":"2015","unstructured":"Park PG, Lee W, Lee SY (2015) Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems. J Franklin Inst 352(4):1378\u20131396","journal-title":"J Franklin Inst"},{"issue":"1","key":"7177_CR30","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.sysconle.2015.03.007","volume":"81","author":"A Seuret","year":"2015","unstructured":"Seuret A, Gouaisbaut F (2015) Hierarchy of LMI conditions for the stability analysis of time delay systems. Syst Control Lett 81(1):1\u20137","journal-title":"Syst Control Lett"},{"key":"7177_CR31","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1016\/j.neucom.2014.01.024","volume":"138","author":"M-D Ji","year":"2014","unstructured":"Ji M-D, He Y, Zhang C-K, Wu M (2014) Novel stability criteria for recurrent neural networks with variable delay. Neurocomputing 138:383\u2013391","journal-title":"Neurocomputing"},{"issue":"7","key":"7177_CR32","doi-asserted-by":"publisher","first-page":"1486","DOI":"10.1109\/TNNLS.2015.2449898","volume":"27","author":"C-K Zhang","year":"2016","unstructured":"Zhang C-K, He Y, Jiang L, Wu M (2016) Stability analysis for delayed neural networks considering both conservativeness and complexity. IEEE Trans Neural Netw Learn Syst 27(7):1486\u20131501","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"10","key":"7177_CR33","first-page":"5937","volume":"218","author":"Y Liu","year":"2012","unstructured":"Liu Y, Hu L-S, Shi P (2012) A novel approach on stabilization for linear systems with variable input delay. Appl Math Comput 218(10):5937\u20135947","journal-title":"Appl Math Comput"},{"issue":"8","key":"7177_CR34","doi-asserted-by":"publisher","first-page":"1947","DOI":"10.1007\/s00521-011-0598-2","volume":"21","author":"W Hu","year":"2012","unstructured":"Hu W, Li C, Wu S (2012) Stochastic robust stability for neutral-type impulsive interval neural networks with distributed time-varying delays. Neural Comput Appl 21(8):1947\u20131960","journal-title":"Neural Comput Appl"},{"issue":"3","key":"7177_CR35","doi-asserted-by":"publisher","first-page":"336","DOI":"10.1109\/TNB.2014.2327582","volume":"13","author":"W Zhang","year":"2014","unstructured":"Zhang W, Tang Y, Wu X, Fang J-A (2014) Stochastic stability of switched genetic regulatory networks with time-varying delays. IEEE Trans Nanobiosci 13(3):336\u2013342","journal-title":"IEEE Trans Nanobiosci"},{"issue":"3","key":"7177_CR36","doi-asserted-by":"publisher","first-page":"899","DOI":"10.1016\/j.neucom.2015.08.045","volume":"173","author":"W Wang","year":"2016","unstructured":"Wang W, Wang Y, Nguang SK, Zhong S, Liu F (2016) Delay partition method for the robust stability of uncertain genetic regulatory networks with variable delays. Neurocomputing 173(3):899\u2013911","journal-title":"Neurocomputing"},{"key":"7177_CR37","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/j.neucom.2012.03.014","volume":"93","author":"W Wang","year":"2012","unstructured":"Wang W, Zhong S, Liu F (2012) New delay-dependent stability criteria for uncertain genetic regulatory networks with variable delays. Neurocomputing 93:19\u201326","journal-title":"Neurocomputing"},{"key":"7177_CR38","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1016\/j.mbs.2016.02.006","volume":"275","author":"H Moradi","year":"2016","unstructured":"Moradi H, Majd VJ (2016) Robust control of uncertain nonlinear switched genetic regulatory networks with time delays: A redesign approach. Math Biosci 275:10\u201317","journal-title":"Math Biosci"},{"issue":"1","key":"7177_CR39","doi-asserted-by":"publisher","first-page":"118","DOI":"10.1109\/TNNLS.2016.2614709","volume":"29","author":"Y Liu","year":"2018","unstructured":"Liu Y, Guo B-Z, Park JH, Lee S-M (2018) Nonfragile exponential synchronization of delayed complex dynamical networks with memory sampled-data control. IEEE Trans Neural Netw Learn Syst 29(1):118\u2013128","journal-title":"IEEE Trans Neural Netw Learn Syst"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-022-07177-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00521-022-07177-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-022-07177-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,24]],"date-time":"2022-07-24T10:08:11Z","timestamp":1658657291000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00521-022-07177-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,31]]},"references-count":39,"journal-issue":{"issue":"16","published-print":{"date-parts":[[2022,8]]}},"alternative-id":["7177"],"URL":"https:\/\/doi.org\/10.1007\/s00521-022-07177-6","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"type":"print","value":"0941-0643"},{"type":"electronic","value":"1433-3058"}],"subject":[],"published":{"date-parts":[[2022,3,31]]},"assertion":[{"value":"18 September 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 March 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 March 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declared that they have no conflict of interest to this work.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}