Models of Chemical Reaction Systems with Exactly Evaluable Limit Cycle Oscillations and their Bifurcation Behaviour

Abstract

AbstractModels of open chemical reaction systems with two variables x,y and with elliptic limit cycles in concentration space are investigated. Thereby isothermal and homogeneous conditions and the validity of mass‐action kinetics are assumed. Though we restrict ourselves to quadratic rate equations a lot of systems with this behaviour is found; all based on the trimolecular reaction A + 2X → 3X. Both globally stable and only locally stable limit cycles are possible. The time dependence of the variables on the cycle is exactly evaluated for all these systems. By means of simple examples both Hopf bifurcation and other types of transition of the limit cycle are studied analytically. Finally the qualitatively different properties of these transitions are pointed out in a table.