{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T23:01:10Z","timestamp":1773615670657,"version":"3.50.1"},"reference-count":21,"publisher":"Allerton Press","issue":"7","license":[{"start":{"date-parts":[[2020,12,1]],"date-time":"2020-12-01T00:00:00Z","timestamp":1606780800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2020,12,1]],"date-time":"2020-12-01T00:00:00Z","timestamp":1606780800000},"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":["Aut. Control Comp. Sci."],"published-print":{"date-parts":[[2020,12]]},"DOI":"10.3103\/s0146411620070081","type":"journal-article","created":{"date-parts":[[2021,2,8]],"date-time":"2021-02-08T12:46:46Z","timestamp":1612788406000},"page":"655-684","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A New Approach to Gene Network Modeling"],"prefix":"10.3103","volume":"54","author":[{"given":"S. D.","family":"Glyzin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. Yu.","family":"Kolesov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"N. Kh.","family":"Rozov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1627","published-online":{"date-parts":[[2021,2,8]]},"reference":[{"key":"7283_CR1","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1038\/35002125","volume":"403","author":"M.B. Elowitz","year":"2000","unstructured":"Elowitz, M.B. and Leibler, S., A synthetic oscillatory network of transcriptional regulators, Nature, 2000, vol.\u00a0403, pp. 335\u2013338.","journal-title":"Nature"},{"key":"7283_CR2","first-page":"575","volume":"31","author":"A.N. Tikhonov","year":"1952","unstructured":"Tikhonov, A.N., Systems of differential equations containing small parameters in the derivatives, Mat. Sb., 1952, vol. 31, no. 3, pp. 575\u2013586.","journal-title":"Mat. Sb."},{"key":"7283_CR3","first-page":"57","volume":"7","author":"E.P. Volokitin","year":"2004","unstructured":"Volokitin, E.P., On limit cycles in the simplest model of a hypothetical gene network, Sib. Zh. Ind. Mat., 2004, vol. 7, no. 3, pp. 57\u201365.","journal-title":"Sib. Zh. Ind. Mat."},{"key":"7283_CR4","doi-asserted-by":"publisher","first-page":"4097","DOI":"10.1142\/S0218127409025237","volume":"19","author":"O. Buse","year":"2009","unstructured":"Buse, O., Kuznetsov, A., and P\u00e9rez, R.A., Existence of limit cycles in the repressilator equations, Int. J. Bifurcation Chaos, 2009, vol. 19, no. 12, pp. 4097\u20134106.","journal-title":"Int. J. Bifurcation Chaos"},{"key":"7283_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1103\/PhysRevE.81.066206","volume":"81","author":"O. Buse","year":"2010","unstructured":"Buse, O., P\u00e9rez, R., and Kuznetsov, A., Dynamical properties of the repressilator model, Phys. Rev. E, 2010, vol. 81, pp. 066206-1\u2013066206-7.","journal-title":"Phys. Rev. E"},{"key":"7283_CR6","first-page":"64","volume":"6","author":"V.A. Likhoshvai","year":"2003","unstructured":"Likhoshvai, V.A., Matushkin, Yu.G., and Fadeev, S.I., Problems in the theory of the functioning of genetic networks, Sib. Zh. Ind. Mat., 2003, vol. 6, no. 2, pp. 64\u201380.","journal-title":"Sib. Zh. Ind. Mat."},{"key":"7283_CR7","first-page":"2166","volume":"44","author":"G.V. Demidenko","year":"2004","unstructured":"Demidenko, G.V., Kolchanov, N.A., Likhoshvai, V.A., Matushkin, Yu.G., and Fadeev, S.I., Mathematical modeling of regular contours of gene networks, Comput. Math. Math. Phys., 2004, vol. 44, no. 12, pp. 2166\u20132183.","journal-title":"Comput. Math. Math. Phys."},{"key":"7283_CR8","first-page":"134","volume":"6","author":"S.I. Fadeev","year":"2003","unstructured":"Fadeev, S.I. and Likhoshvai, V.A., On hypothetical gene networks, Sib. Zh. Ind. Mat., 2003, vol. 6, no. 3, pp.\u00a0134\u2013153.","journal-title":"Sib. Zh. Ind. Mat."},{"key":"7283_CR9","doi-asserted-by":"crossref","unstructured":"Kolesov, A.Yu., Rozov, N.Kh., and Sadovnichii, V.A., Periodic solutions of travelling-wave type in circular gene networks, Izv. Math., 2016, vol. 80, vol. 3, pp. 523\u2013548.","DOI":"10.1070\/IM8398"},{"key":"7283_CR10","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1134\/S0001434617010072","volume":"101","author":"S.D. Glyzin","year":"2017","unstructured":"Glyzin, S.D., Kolesov, A.Yu., and Rozov, N.Kh., Existence and stability of the relaxation cycle in a mathematical repressilator model, Math. Notes, 2017, vol. 101, no. 1, pp. 71\u201386.","journal-title":"Math. Notes"},{"key":"7283_CR11","doi-asserted-by":"publisher","first-page":"1724","DOI":"10.1134\/S0965542506100101","volume":"46","author":"S.D. Glyzin","year":"2006","unstructured":"Glyzin, S.D., Kolesov, A.Yu., and Rozov, N.Kh., Chaos phenomena in a circle of three unidirectionally connected oscillators, Comput. Math. Math. Phys., 2006, vol. 46, no. 10, pp. 1724\u20131736.","journal-title":"Comput. Math. Math. Phys."},{"key":"7283_CR12","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1142\/S0218127494000356","volume":"4","author":"T. Kapitaniak","year":"1994","unstructured":"Kapitaniak, T. and Chua, L.O., Hyperchaotic attractors of unidirectionally-coupled Chua\u2019s circuits, Int. J. Bifurcation Chaos, 1994, vol. 4, no. 2, pp. 477\u2013482.","journal-title":"Int. J. Bifurcation Chaos"},{"key":"7283_CR13","doi-asserted-by":"publisher","first-page":"224","DOI":"10.1016\/S0167-2789(98)00303-0","volume":"128","author":"I.P. Mari\u00f1o","year":"1999","unstructured":"Mari\u00f1o, I.P., P\u00e9rez-Mu\u00f1uzuri, V., P\u00e9rez-Villar, V., S\u00e1nchez, E., and Mat\u00edas, M.A., Interaction of chaotic rotating waves in coupled rings of chaotic cells, Phys. D, 1999, vol. 128, pp. 224\u2013235.","journal-title":"Phys. D"},{"key":"7283_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1063\/1.3293176","volume":"20","author":"P. Perlikowski","year":"2010","unstructured":"Perlikowski, P., Yanchuk, S., Wolfrum, M., Stefanski, A., Mosiolek, P., and Kapitaniak, T., Routes to complex dynamics in a ring of unidirectionally coupled systems, Chaos, 2010, vol. 20, pp. 1\u201310.","journal-title":"Chaos"},{"key":"7283_CR15","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1134\/S0040577918030121","volume":"194","author":"S.D. Glyzin","year":"2018","unstructured":"Glyzin, S.D., Kolesov, A.Yu., and Rozov, N.Kh., An approach to modeling artificial gene networks, Theor. Math. Phys., 2018, vol. 194, no. 3, pp. 471\u2013490.","journal-title":"Theor. Math. Phys."},{"key":"7283_CR16","doi-asserted-by":"publisher","first-page":"659","DOI":"10.1134\/S0965542518050093","volume":"58","author":"S.D. Glyzin","year":"2018","unstructured":"Glyzin, S.D., Kolesov, A.Yu., and Rozov, N.Kh., Quasi-stable structures in circular gene networks Comput. Math. Math. Phys., 2018, vol. 58, no. 5, pp. 659\u2013679.","journal-title":"Comput. Math. Math. Phys."},{"key":"7283_CR17","doi-asserted-by":"crossref","unstructured":"Glyzin, S.D., Kolesov, A.Yu., and Rozov, N.Kh., Quasi-stable solutions of the genetic networks models, J.\u00a0Phys.: Conf. Ser., 2019, vol. 1163.","DOI":"10.1088\/1742-6596\/1163\/1\/012070"},{"key":"7283_CR18","first-page":"1","volume":"199","author":"A.Yu. Kolesov","year":"1995","unstructured":"Kolesov, A.Yu. and Kolesov, Yu.S., Relaxational oscillations in mathematical models of ecology, Proc. Steklov Inst. Math., 1995, vol. 199, pp. 1\u2013126.","journal-title":"Proc. Steklov Inst. Math."},{"key":"7283_CR19","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1070\/IM2013v077n02ABEH002636","volume":"77","author":"S.D. Glyzin","year":"2013","unstructured":"Glyzin, S.D., Kolesov, A.Yu., and Rozov, N.Kh., Relaxation self-oscillations in Hopfield networks with delay, Izv. Math., 2013, vol. 77, no. 2, pp. 271\u2013312.","journal-title":"Izv. Math."},{"key":"7283_CR20","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1007\/s11232-013-0041-1","volume":"175","author":"S.D. Glyzin","year":"2013","unstructured":"Glyzin, S.D., Kolesov, A.Yu., and Rozov, N.Kh., Periodic traveling-wave-type solutions in circular chains of unidirectionally coupled equations, Theor. Math. Phys., 2013, vol. 175, no. 1, pp. 499\u2013517.","journal-title":"Theor. Math. Phys."},{"key":"7283_CR21","doi-asserted-by":"publisher","first-page":"708","DOI":"10.1070\/IM2014v078n04ABEH002704","volume":"78","author":"S.D. Glyzin","year":"2014","unstructured":"Glyzin, S.D., Kolesov, A.Yu., and Rozov, N.Kh., The buffer phenomenon in ring-like chains of unidirectionally connected generators, Izv. Math., 2014, vol. 78, no. 4, pp. 708\u2013743.","journal-title":"Izv. Math."}],"container-title":["Automatic Control and Computer Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.3103\/S0146411620070081.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.3103\/S0146411620070081","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.3103\/S0146411620070081.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T22:03:05Z","timestamp":1773612185000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.3103\/S0146411620070081"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12]]},"references-count":21,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2020,12]]}},"alternative-id":["7283"],"URL":"https:\/\/doi.org\/10.3103\/s0146411620070081","relation":{},"ISSN":["0146-4116","1558-108X"],"issn-type":[{"value":"0146-4116","type":"print"},{"value":"1558-108X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12]]},"assertion":[{"value":"5 August 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 September 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 September 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 February 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare that they have no conflicts of interest.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"CONFLICT OF INTEREST"}},{"value":"Sergey D. Glyzin, orcid.org\/0000-0002-6403-4061, professor.Andgey Yu. Kolesov, orcid.org\/0000-0001-5066-0881, professor.Nikolay Kh. Rozov, orcid.org\/0000-0002-9330-549X, professor.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"ADDITIONAL INFORMATION"}}]}}