Open AccessBifurcation and chaos in a pulsed plankton model with instantaneous nutrient recycling
Author(s) -
Sanling Yuan,
Yu Zhao,
Anfeng Xiao,
Tonghua Zhang
Publication year - 2012
Publication title -
the rocky mountain journal of mathematics/rocky mountain journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.374
H-Index - 42
eISSN - 1945-3795
pISSN - 0035-7596
DOI - 10.1216/rmj-2012-42-4-1387
Subject(s) - mathematics , bifurcation , chaos (operating system) , plankton , nutrient , ecology , biology , nonlinear system , physics , computer science , computer security , quantum mechanics
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