Nutrient-phytoplankton-zooplankton interaction with variable yields

Joydeb Bhattacharyya¹ ; Samares Pal¹

¹ Department of Mathematics University of Kalyani Kalyani 741235, India

Applicationes Mathematicae, Tome 40 (2013) no. 3, pp. 327-349

Résumé

A three dimensional predator-prey-resource model is proposed and analyzed to study the dynamics of the system with resource-dependent yields of the organisms. Our analysis leads to different thresholds in terms of the model parameters acting as conditions under which the organisms associated with the system cannot thrive even in the absence of predation. Local stability of the system is obtained in the absence of one or more of the predators and in the presence of all the predators. Under appropriate circumstances global stability of the system is obtained in the absence of the predator at the highest trophic level. Moreover, it is shown that the system undergoes Hopf bifurcation if the break-even concentration crosses a certain critical value. Computer simulations have been carried out to illustrate various analytical results.

Détail

DOI : 10.4064/am40-3-5

Keywords: three dimensional predator prey resource model proposed analyzed study dynamics system resource dependent yields organisms analysis leads different thresholds terms model parameters acting conditions under which organisms associated system cannot thrive even absence predation local stability system obtained absence predators presence predators under appropriate circumstances global stability system obtained absence predator highest trophic level moreover shown system undergoes hopf bifurcation break even concentration crosses certain critical value computer simulations have carried out illustrate various analytical results