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- W2053643041 abstract "In this paper we continue work on the simplified model of G.I. Bell, which simulates an immune response. It is shown that for certain parametric values, there exists a closed separatrix in the phase plane. Conditions are given under which this closed separatrix is stable or unstable. Then a bifurcation theorem of Andronov and Leontovich is used to show how larger amplitude periodic solutions branch from this closed separatrix. There follows an extension of continuous families of periodic solutions to maximal families (in the product of the phase space with a parametric dimension). Such an extension has a unique terminating closed solution; either a closed separatrix, a periodic solution, or the stationary solution. Then it is indicated the types of secondary bifurcation behavior that can occur at the terminating solution of a continuous family of periodic solutions if this terminating solution is itself a nontrivial periodic solution. The paper ends with a general discussion of these matters, with possible biomedical consequences. The question of secondary bifurcation, which arises quite generally in other nonlinear problems as well, is as yet Terra incognita." @default.
- W2053643041 created "2016-06-24" @default.
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- W2053643041 date "1974-12-01" @default.
- W2053643041 modified "2023-09-28" @default.
- W2053643041 title "Periodic solutions of predator-prey equations simulating an immune response, II" @default.
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- W2053643041 doi "https://doi.org/10.1016/0025-5564(74)90019-4" @default.
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