Dynamic complexities of predator–prey system in a pulsed chemostat

• Published in: Communications in nonlinear science & numerical simulation Vol. 17; no. 6; pp. 2489 - 2500
• Main Authors: Jia, Jianwen, Zhang, HongHong
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.06.2012
• Subjects: Bifurcation; Bifurcations; Boundaries; Chemostat model; Dynamical systems; Impulsive differential equation; Mathematical models; Nonlinear dynamics; Oscillations; Periodic solution; Predators; Impulsive differential equation; Bifurcation; Periodic solution; Chemostat model
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2011.06.027

► Different types of functional responses are considered in the food chain chemostat model. ► In addition, variable yield and pulsed input are included in the model, which are more reasonable. ► Using standard techniques of bifurcation theory, we get a threshold and above which periodic oscillations will exist. ► Numerical simulations are carried out to illustrate our theoretical results. ► By comparing bifurcation diagrams, we can see that the system shows two kinds of bifurcations. In this paper, we study a food chain model with Holling III and Monod type functional response under periodic pulsed conditions, which contains with predator, prey and periodically pulsed substrate. We investigate the subsystem with substrate and prey and study the stability of the boundary periodic solution. By use of standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in prey and predator. Furthermore, by comparing bifurcation diagrams with different bifurcation parameters, we can see that the system shows two kinds of bifurcations, whose are period-doubling and period-halving.