Biochemical systems as generators of local and global limit cycles

It has recently been noted (8) that the global limit cycle (hard self-excitation) is apparently not uncommon in nature, especially in biochemical systems. This idea is confirmed by a more detailed study of many biochemical systems with quite different topological structures. The present paper describes some of the cases considered; they were deliberately chosen to be simple, but they almost all have the following properties: for one set of parameters, the linearization method shows that there is a local limit cycle (soft self-excitation); for other parameters, the systems may have global limit cycles.