Abstract
For a class of dynamical systems of the form \(\dot x = q{\text{(}}x{\text{)}} - u{\text{(}}x,y{\text{)}},\;\;\dot y = \varepsilon {\text{(}}v{\text{(}}x,y) - r(y))\), we prove boundedness of all solutions in the positive time direction. We discuss the existence of stable limit cycles for the simplest autocatalytic reaction involving two internal and two external reactants, as well as for a number of other models arising in applications.
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Erle, D. A boundedness theorem with application to oscillation of autocatalytic chemical reactions. Journal of Mathematical Chemistry 24, 365–378 (1998). https://doi.org/10.1023/A:1019147408848
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DOI: https://doi.org/10.1023/A:1019147408848