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.
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Escher, C. Global stability analysis of open two-variable quadratic mass-action systems with elliptical limit cycles. Z. Physik B - Condensed Matter 40, 137–141 (1980). https://doi.org/10.1007/BF01295082
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DOI: https://doi.org/10.1007/BF01295082