{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:12:02Z","timestamp":1753884722698,"version":"3.41.2"},"reference-count":30,"publisher":"World Scientific Pub Co Pte Ltd","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2022,9,15]]},"abstract":"<jats:p> In this study, a uniformly distributed mathematical model for the self-heating process within compost piles is formulated and investigated. It consists of mass balance equations for oxygen and energy as well as the heat-generation processes due to both biological and chemical activities. This model is an extension of the study of Luangwilai et al. [2013] which consists of only biological activity. The singularity and degenerate Hopf bifurcation theories are used to determine the loci of different singularities: the isola, cusp, double-limit points and boundary limit set as well as the double-Hopf, generalized Hopf (Bautin) and Bogdanov\u2013Takens bifurcations. In this investigation it is found that these loci separate the secondary parameter plane into twenty-two regions of different steady-state solution behaviors, whereas the model in the earlier study reported only eight regions. With more topological detail in the parameter space, a clearer understanding of the thermal behavior of a compost pile can be obtained, thus assisting compost operators in controlling the temperature within the pile more effectively: for example, achieving desirable elevated temperature range for ideal composting conditions via periodic solutions and S-shaped solution branch, or alternatively, understanding conditions, if not monitored carefully, that can also increase the likelihood of spontaneous ignition within the pile. <\/jats:p>","DOI":"10.1142\/s0218127422300270","type":"journal-article","created":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T08:12:40Z","timestamp":1664439160000},"source":"Crossref","is-referenced-by-count":0,"title":["Inclusion of Biological and Chemical Self-Heating Processes in Compost Piles Model: A Semenov Formulation"],"prefix":"10.1142","volume":"32","author":[{"given":"T.","family":"Luangwilai","sequence":"first","affiliation":[{"name":"Mathematics and Computer Science Division, Navaminda Kasatriyadhiraj Royal Thai Air Force Academy, Bangkok, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H. 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