Analysis of Monod type food chain chemostat with k-times’ periodically pulsed input

• Published in: Journal of mathematical chemistry 2008-05, Vol.43 (4), p.1371-1388
• Main Authors: Pang, Guoping, Liang, Yanlai, Wang, Fengyan
• Format: Article
• Language: English
• Subjects: Chemistry; Chemistry and Materials Science; Exact sciences and technology; General and physical chemistry; Global analysis, analysis on manifolds; Math. Applications in Chemistry; Mathematical analysis; Mathematics; Operator theory; Physical Chemistry; Sciences and techniques of general use; Theoretical and Computational Chemistry; Theory of reactions, general kinetics. Catalysis. Nomenclature, chemical documentation, computer chemistry; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
• ISSN: 0259-9791; 1572-8897
• DOI: 10.1007/s10910-007-9258-2

In this paper, we introduce and study a model of a predator-prey system with Monod type functional response under periodic pulsed chemostat conditions, which contains with predator, prey, and periodically pulsed substrate. We investigate the subsystem with substrate and prey and study the stability of the periodic solutions, which are the boundary periodic solutions of the system. The stability analysis of the boundary periodic solution yields an invasion threshold. By use of standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in substrate, prey and predator. Simple cycles may give way to chaos in a cascade of period-doubling bifurcations. Furthermore, by comparing bifurcation diagrams with different bifurcation parameters, we can see that the impulsive system shows two kinds of bifurcations, whose are period-doubling and period-halfing.