Three limit cycles for a first-order exothermic chemical reaction in a continuous stirred-tank reactor

Abstract

We study a first‐order exothermic chemical reaction in a continuous stirred‐tank reactor modelled by a 3‐parameter family of vector fields in \(\mathbb{R}^2 \). We prove that there exist regions in \(\mathbb{R}^3 \) which contain points that depend on parameters such that the chemical reaction has 0, 1, 2, or 3 small amplitude limit cycles that surround the origin. We conclude that this model can reach two stable small amplitude limit cycles. Finally, we show that one of these regions contains the point in the parameter space considered by Gurel and Lapidus [6] who proved numerically the existence of one stable limit cycle.