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.
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Hering, R.H. Oscillations in Lotka-Volterra systems of chemical reactions. J Math Chem 5, 197–202 (1990). https://doi.org/10.1007/BF01166429
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DOI: https://doi.org/10.1007/BF01166429