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Transcritical bifurcation and saddle-node bifurcation are studied in the vector fields restricted to the corresponding center manifolds. Hopf bifurcation is analyzed in the frequency domain. In particular, the sixth-order harmonic balance approximations to the frequency and the amplitude of the periodic solutions, and the analytical expressions for these solutions are given. Numerical simulation study demonstrates various types of bifurcations and the complex solution behaviors, such as cyclic fold bifurcation, period-doubling bifurcation, period-doubling cascade and chaotic orbits. All these results complement previous theoretical studies on the model, and contribute to a better understanding of the qualitative dynamics of the cancer model. <\/jats:p>","DOI":"10.1142\/s0218127420500248","type":"journal-article","created":{"date-parts":[[2020,3,10]],"date-time":"2020-03-10T09:56:49Z","timestamp":1583834209000},"page":"2050024","source":"Crossref","is-referenced-by-count":9,"title":["Bifurcation Analysis in a Cancer Growth Model"],"prefix":"10.1142","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5572-467X","authenticated-orcid":false,"given":"Yu","family":"Chang","sequence":"first","affiliation":[{"name":"College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoli","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, P. R. 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