科研之友
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摘要
There have been some results on bifurcations of codimension one (such as saddle-node, transcritical, pitchfork) and degenerate Hopf bifurcations for an enzyme-catalyzed reaction system comprising a branched network but no further discussion for bifurcations at its cusp. In this paper we give conditions for the existence of a cusp and compute the parameter curves for the Bogdanov-Takens bifurcation, which induces the appearance of homoclinic orbits and periodic orbits, indicating the tendency to steady-states or a rise of periodic oscillations for the concentrations of the substrate and the product.
