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- W2203977075 abstract "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–transcritical interaction and the Hopf–transcritical 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–Volterra model and to an infection model in HIV diseases." @default.
- W2203977075 created "2016-06-24" @default.
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- W2203977075 date "2015-06-15" @default.
- W2203977075 modified "2023-09-25" @default.
- W2203977075 title "Dynamical Systems with a Codimension-One Invariant Manifold: The Unfoldings and Its Bifurcations" @default.
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- W2203977075 doi "https://doi.org/10.1142/s0218127415500911" @default.
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