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- W2080159910 abstract "We study the Hopf bifurcation of C3 differential systems in Rn showing that l limit cycles can bifurcate from one singularity with eigenvalues ±bi and n - 2 zeros with l in {0,1,�,2n-3}. As far as we know this is the first time that it is proved that the number of limit cycles that can bifurcate in a Hopf bifurcation increases exponentially with the dimension of the space. To prove this result, we use first-order averaging theory. Further, in dimension 4 we characterize the shape and the kind of stability of the bifurcated limit cycles. We apply our results to certain fourth-order differential equations and then to a simplified Marchuk model that describes immune response." @default.
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- W2080159910 date "2009-03-04" @default.
- W2080159910 modified "2023-09-27" @default.
- W2080159910 title "Hopf bifurcation in higher dimensional differential systems via the averaging method" @default.
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- W2080159910 doi "https://doi.org/10.2140/pjm.2009.240.321" @default.
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