caa a22 4500 477140572 CHVBK 20180405111731.0 cr unu---uuuuu 170330e19971101xx s 000 0 eng 10.1007/s002850050093 doi (NATIONALLICENCE)springer-10.1007/s002850050093 Local and global bifurcations at infinity in models of glycolytic oscillations [Elektronische Daten] [J. Sturis, M. Brøns] Abstract.:  We investigate two models of glycolytic oscillations. Each model consists of two coupled nonlinear ordinary differential equations. Both models are found to have a saddle point at infinity and to exhibit a saddle-node bifurcation at infinity, giving rise to a second saddle and a stable node at infinity. Depending on model parameters, a stable limit cycle may blow up to infinite period and amplitude and disappear in the bifurcation, and after the bifurcation, the stable node at infinity then attracts all trajectories. Alternatively, the stable node at infinity may coexist with either a stable sink (not at infinity) or a stable limit cycle. This limit cycle may then disappear in a heteroclinic bifurcation at infinity in which the unstable manifold from one saddle at infinity joins the stable manifold of the other saddle at infinity. These results explain prior reports for one of the models concerning parameter values for which the system does not admit any physical (bounded) behavior. Analytic results on the scaling of amplitude and period close to the bifurcations are obtained and confirmed by numerical computations. Finally, we consider more realistic modified models where all solutions are bounded and show that some of the features stemming from the bifurcations at infinity are still present. Springer-Verlag Berlin Heidelberg, 1997 Sturis J. Scientific Computing, Novo Nordisk, DK-2880 BagsvæGrd, Denmark, DK aut Brøns M. Department of Mathematics, Technical University of Denmark, DK-2800 Lyngby, Denmark, DK aut https://doi.org/10.1007/s002850050093 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s002850050093 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Sturis J. Scientific Computing, Novo Nordisk, DK-2880 BagsvæGrd, Denmark, DK aut NATIONALLICENCE 700 1- Brøns M. Department of Mathematics, Technical University of Denmark, DK-2800 Lyngby, Denmark, DK aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer