کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4615867 | 1339331 | 2014 | 21 صفحه PDF | دانلود رایگان |
In this paper, a phytoplankton–zooplankton model with toxic liberation delay is considered. Firstly, the critical values of Hopf bifurcation, transcritical bifurcation and Hopf-transcritical bifurcation are given, and to give more detailed information about the periodic oscillations, the direction and stability of Hopf bifurcation is studied by using the normal-form theory and center manifold theorem. Then, we give the detailed bifurcation set by calculating the universal unfoldings near the Hopf-transcritical bifurcation point. Finally, we show that the plankton system may exhibit quasi-periodic oscillations, which are verified both theoretically and numerically, and explain the experimental observed fluctuation phenomenon of plankton population.
Journal: Journal of Mathematical Analysis and Applications - Volume 415, Issue 2, 15 July 2014, Pages 574–594