Abstract
Limit cycles are sought in a mathematical model of a simple hypothetical chemical reaction involving essentially only two reacting species. Physically, these limit cycles correspond to time-periodic oscillations in the concentrations of the two chemicals. A combination of analytical and numerical methods reveals that limit-cycle behaviour is only possible in a restricted region of the parameter space. Strong numerical evidence is presented to assert that the limit cycle is unique and stable to infinitesimal perturbations. Numerical solutions are displayed and discussed.
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Forbes, L.K., Holmes, C.A. Limit-cycle behaviour in a model chemical reaction: the cubic autocatalator. J Eng Math 24, 179–189 (1990). https://doi.org/10.1007/BF00129873
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DOI: https://doi.org/10.1007/BF00129873