{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,3,23]],"date-time":"2023-03-23T08:54:44Z","timestamp":1679561684346},"reference-count":32,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2015,6,15]]},"abstract":"<jats:p> We investigate a dynamical system having a special structure namely a codimension-one invariant manifold that is preserved under the variation of parameters. We derive conditions such that bifurcations of codimension-one and of codimension-two occur in the system. The normal forms of these bifurcations are derived explicitly. Both local and global bifurcations are analyzed and yield the transcritical bifurcation as the codimension-one bifurcation while the saddle-node\u2013transcritical interaction and the Hopf\u2013transcritical interactions as the codimension-two bifurcations. The unfolding of this degeneracy is also analyzed and reveal global bifurcations such as homoclinic and heteroclinic bifurcations. We apply our results to a modified Lotka\u2013Volterra model and to an infection model in HIV diseases. <\/jats:p>","DOI":"10.1142\/s0218127415500911","type":"journal-article","created":{"date-parts":[[2015,6,16]],"date-time":"2015-06-16T22:48:21Z","timestamp":1434494901000},"page":"1550091","source":"Crossref","is-referenced-by-count":6,"title":["Dynamical Systems with a Codimension-One Invariant Manifold: The Unfoldings and Its Bifurcations"],"prefix":"10.1142","volume":"25","author":[{"given":"Kie Van Ivanky","family":"Saputra","sequence":"first","affiliation":[{"name":"Department of Mathematics, Universitas Pelita Harapan, Jl. 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