{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T15:47:59Z","timestamp":1760888879990,"version":"3.40.4"},"reference-count":22,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2014,3]]},"abstract":"<jats:p>We study the Hopf bifurcation for a class of three-dimensional cubic Kolmogorov model by making use of our method (i.e. singular values method). We show that the positive singular point (1, 1, 1) of an investigated model can become a fine focus of 5 order, and moreover, it can bifurcate five small limit cycles under certain coefficients with disturbed condition. In terms of three-dimensional cubic Kolmogorov model, published references can hardly be seen, and our results are new. At the same time, it is worth pointing out that our method is valid to study the Hopf bifurcation problem for other three-dimensional polynomial differential systems.<\/jats:p>","DOI":"10.1142\/s0218127414500369","type":"journal-article","created":{"date-parts":[[2014,3,25]],"date-time":"2014-03-25T09:36:36Z","timestamp":1395740196000},"page":"1450036","source":"Crossref","is-referenced-by-count":14,"title":["Three-Dimensional Hopf Bifurcation for a Class of Cubic Kolmogorov Model"],"prefix":"10.1142","volume":"24","author":[{"given":"Chaoxiong","family":"Du","sequence":"first","affiliation":[{"name":"Department of Mathematics, Hunan Shaoyang University, Shaoyang, Hunan 422000, P. R. China"}]},{"given":"Qinlong","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hezhou University, Hezhou, Guangxi 542800, P. R. 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