Generalized normal sectors and orbits in exceptional directions. (English) Zbl 1089.34028
Summary: A method of so-called ‘generalized normal sectors’ is developed for determining orbits in exceptional directions near high degenerate equilibria for which the well-known methods of normal sectors and Z-sectors are not applicable so that a more extensive class of degenerate equilibria can be discussed for qualitative properties. Our method proves to be effective in the study of high degenerate equilibria in a multimolecular reaction system at infinity and in a ratio-dependent predator-prey system.
MSC:
34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
92D25 | Population dynamics (general) |
80A30 | Chemical kinetics in thermodynamics and heat transfer |