Global stability analysis of open two-variable quadratic mass-action systems with elliptical limit cycles

Abstract

We consider open, isothermal and homogeneous two-variable quadratic mass-action systems which exhibit sustained oscillations on an ellipse in phase space [1]. To each system with an elliptic limit cycle there corresponds a conservative one the trajectories of which are curves without contact for the limit cycle system [2]. These trajectories, i.e., the trajectories of all systems oscillating conservatively on an ellipse, are computed analytically. Thus a global stability analysis of every system with an elliptic limit cycle can be performed.