title: Local and global limit cycles in biochemical systems.
abstract: An autonomous periodic behaviour may correspond to a local or global limit cycle. If the cycle is local, the mathematical analysis is fairly easy upon linearizing about a singular point, but there are few mathematical methods for the determination of global limiting cycles. A periodic motion has a priori a 50% chance of being global. This paper describes a method of predicting certain types of global limit cycles. The application of this procedure indicates that there are plenty of biochemical systems with stable singular points but nevertheless oscillatory.
mesh_terms: D002384:Catalysis; D004798:Enzymes / Q000378:metabolism*; D007700:Kinetics; D008433:Mathematics; D008954:Models, Biological; D010507:Periodicity
chemical_list: D004798:Enzymes