Stability and bifurcation analysis of a modified chemostat model

In this work, we derive a discrete-time chemostat model from a continuous-time population model using the forward Euler method. We first determine the model’s fixed points and analyze their local stability. By applying the central manifold theorem and bifurcation theory, we establish the existence of flip and Neimark-Sacker bifurcations, considering the step size as the bifurcation parameter. Theoretical findings are validated through numerical simulations, which also uncover novel dynamic behaviors.