×

Positive and negative circuits in dynamical systems. (English) Zbl 1058.37537

Summary: We state precisely and demonstrate two conjectures of R. Thomas following which (a) the existence of a positive circuit in the oriented interaction graph of a differential system is a necessary condition for the existence of several steady states, and (b) the existence of a negative non-oriented circuit of length at least two is a necessary condition for the existence of a stable periodic orbit.

MSC:

37N25 Dynamical systems in biology
PDFBibTeX XMLCite
Full Text: DOI