Abstract
For a chemical reaction system modeled byx =k 1 Ax −k 2 x 2 −k 3 xy +k 4 y 2,y =k 3 xy −k 4 y 2 −k 5 y +k 6 B, it is shown that for each positive choice of parametersk i A, B there exists a unique stationary state which is globally asymptotically stable in the positive quadrant. A criterion for the non-existence of periodic solutions is given for the generalized Lotka-Volterra system:x = f(x)h(x, y),y.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A.A. Andronow and C.E. Chaikin,Theory of Oscillations (Princeton University Press, Princeton, NJ, 1949).
W. Boyce and R. DiPrima,Elementary Differential Equations and Boundary Value Problems (Wiley, New York, 1965).
T.A. Burton,Stability and Periodic Solutions of Ordinary and Functional Differential Equations (Academic Press, New York, 1985).
H. Farkas and Z. Noszticzius, J. Chem. Soc. Faraday Trans. 2, 81 (1985)1487.
T.A. Gribshaw, K. Showalter, D.L. Banville and I.R. Epstein, J. Phys. Chem. 85 (1981)2152.
P. Hanusse, C.R. Acad. Sci. C274 (1972)1245.
R. Lefever, G. Nicolis and I. Prigogine, J. Chem. Phys. 47 (1967)1045.
H.G. Lintz and W. Weber, Chem. Eng. Sci. 35 (1980)203.
A. Lotka, J. Amer. Chem. Soc. 42 (1920)1595.
G. Nicolis and J. Portnow, Chem. Rev. 73 (1973)265.
I. Prigogine,Introduction to Thermodynamics of Irreversible Processes, 3rd Ed (Wiley, New York, 1967).
J.J. Tyson and J.C. Light, J. Chem. Phys. 59 (1973)4164.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hering, R.H. Oscillations in Lotka-Volterra systems of chemical reactions. J Math Chem 5, 197–202 (1990). https://doi.org/10.1007/BF01166429
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01166429