Bifurcation and chaos in a pulsed plankton model with instantaneous nutrient recycling

Author(s)

Yuan, Sanling; Zhao, Yu; Xiao, Anfeng; Zhang, Tonghua

Abstract

This paper deals with a pulsed plankton-nutrient interaction model consisting of phytoplankton, herbivorous zooplankton and dissolved limiting nutrient with general nutrient uptake functions and instantaneous nutrient recycling. We investigate the subsystem with nutrient and phytoplankton and study the stability of the periodic solutions, which are the boundary periodic solutions of the system. Stability analysis of the boundary periodic solution yields the invasion threshold of zooplankton. By use of standard techniques of bifurcation theory, we prove that, above this threshold, there are periodic oscillations in substrate: phytoplankton and zooplankton. 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, which are period-doubling and period-halving.

Publication year

2012

Publication type

Journal article

Source

Rocky Mountain Journal of Mathematics, Vol. 42, no. 4 (2012), pp. 1387-1409

ISSN

0035-7596

Publisher

Rocky Mountain Mathematics Consortium

Copyright

Copyright © 2012 Rocky Mountain Mathematics Consortium.

Details