Nonlinear Dynamics and Chaos Control in a Discrete Sel'kov Model with Substrate Inhibition

An investigation of the dynamic effects of substrate inhibition in a modified Sel’kov model of glycolytic oscillations is presented in this paper. With a saturated nonlinear term in place of classical polynomial feedback, the discrete-time formulation captures enzymatic regulation more realistically. It exhibits complicated dynamics, including period-doubling bifurcations, compared to the classical continuous Sel’kov model, which undergoes Hopf bifurcation. In this study, the model’s behavior is investigated in multiple ways, including fixed point determination, stability assessment based on the Schur-Cohn criterion, and comprehensive numerical bifurcation analysis. Dynamic transitions from stability to periodic cycles, and then to chaos are revealed. Based on a comparative analysis with the classical model, we demonstrate how substrate inhibition induces complex nonlinear behavior through successive bifurcations. A deeper understanding of feedback regulation in biochemical systems can be gained from this study.