Stability and bifurcation analysis of a modified chemostat model
Demonstratio Mathematica, vol.58, no.1, 2025 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 58 Issue: 1
- Publication Date: 2025
- Doi Number: 10.1515/dema-2025-0160
- Journal Name: Demonstratio Mathematica
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Linguistic Bibliography, zbMATH, Directory of Open Access Journals
- Keywords: chemostat model, flip bifurcation, Neimark-Sacker bifurcation, stability
- Uşak University Affiliated: Yes
Abstract
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.