{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T05:16:50Z","timestamp":1772774210568,"version":"3.50.1"},"reference-count":28,"publisher":"World Scientific Pub Co Pte Ltd","issue":"12","funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"crossref","award":["22-21-00546"],"award-info":[{"award-number":["22-21-00546"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2023,9,30]]},"abstract":"<jats:p> In this paper, the complex dynamics of the pulsating regime of combustion waves propagation is numerically investigated within the Zel\u2019dovich\u2013Barenblatt\u2013Dold model with two-step chain-branching reaction mechanism. It is shown that there exists a remarkable similarity in the dynamics of oscillations in this system and one-dimensional discrete-time maps such as the logistic map. In particular, both systems exhibit the period doubling route to chaos and the\u00a0appearance of windows of stability as the bifurcation parameter is increased. For the first time for a model of combustion wave propagation the sequence of windows of stability is demonstrated and classified. Nevertheless, as the activation energy, which is taken as a bifurcation parameter, reaches a critical value corresponding to the dynamical quenching scenario the dynamics of the flame oscillations becomes multidimensional and therefore it cannot be described by a one-dimensional map anymore. The effect of the heat losses is also studied and it is demonstrated that the number of windows of stability decreases, the order of their appearance changes and the dynamical quenching appears for smaller values of the activation energy as the heat losses are increased. <\/jats:p>","DOI":"10.1142\/s0218127423501377","type":"journal-article","created":{"date-parts":[[2023,10,5]],"date-time":"2023-10-05T09:11:02Z","timestamp":1696497062000},"source":"Crossref","is-referenced-by-count":3,"title":["Influence of Heat Loss on the Chaotic Dynamics of Reaction Waves in the Model with Chain-Branching Reaction"],"prefix":"10.1142","volume":"33","author":[{"given":"Maxim","family":"Kuznetsov","sequence":"first","affiliation":[{"name":"Department of Computational and Quantitative Medicine, Division of Mathematical Oncology, City of Hope, Duarte, CA 91010, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrey","family":"Kolobov","sequence":"additional","affiliation":[{"name":"P.N. Lebedev Physical Institute, Russian Academy of Sciences, 53 Leninskiy Prospekt, Moscow 119991, Russian Federation"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5821-8641","authenticated-orcid":false,"given":"Vladimir","family":"Gubernov","sequence":"additional","affiliation":[{"name":"P.N. Lebedev Physical Institute, Russian Academy of Sciences, 53 Leninskiy Prospekt, Moscow 119991, Russian Federation"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrey","family":"Polezhaev","sequence":"additional","affiliation":[{"name":"P.N. Lebedev Physical Institute, Russian Academy of Sciences, 53 Leninskiy Prospekt, Moscow 119991, Russian Federation"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2023,10,5]]},"reference":[{"key":"S0218127423501377BIB001","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/0010-2180(59)90007-0","volume":"3","author":"Barenblatt G. I.","year":"1959","journal-title":"Combust. Flame"},{"key":"S0218127423501377BIB002","first-page":"1302","volume":"24","author":"Belyaev A. F.","year":"1950","journal-title":"Zh. Fiz. Khim."},{"key":"S0218127423501377BIB003","doi-asserted-by":"crossref","first-page":"1335","DOI":"10.1137\/0143089","volume":"43","author":"Buckmaster J.","year":"1983","journal-title":"SIAM J. Appl. Math."},{"key":"S0218127423501377BIB004","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1088\/1364-7830\/7\/1\/310","volume":"7","author":"Dold J. W.","year":"2003","journal-title":"Combust. Th. 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