Zeitschrift für Physik B Condensed Matter

, Volume 35, Issue 4, pp 351–361

Models of chemical reaction systems with exactly evaluable limit cycle oscillations


  • Claus Escher
    • Institut für Theoretische PhysikRheinisch-Westfälische Technische Hochschule Aachen

DOI: 10.1007/BF01332697

Cite this article as:
Escher, C. Z Physik B (1979) 35: 351. doi:10.1007/BF01332697


Models of open chemical reaction systems with two variablesx, 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 reactionA + 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. Bifurcations of the limit cycle are described analytically.

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© Springer-Verlag 1979