کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4500893 | 1320031 | 2008 | 19 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: A comparison of two predator–prey models with Holling’s type I functional response A comparison of two predator–prey models with Holling’s type I functional response](/preview/png/4500893.png)
In this paper, we analyze a laissez-faire predator–prey model and a Leslie-type predator–prey model with type I functional responses. We study the stability of the equilibrium where the predator and prey coexist by both performing a linearized stability analysis and by constructing a Lyapunov function. For the Leslie-type model, we use a generalized Jacobian to determine how eigenvalues jump at the corner of the functional response. We show, numerically, that our two models can both possess two limit cycles that surround a stable equilibrium and that these cycles arise through global cyclic-fold bifurcations. The Leslie-type model may also exhibit super-critical and discontinuous Hopf bifurcations. We then present and analyze a new functional response, built around the arctangent, that smoothes the sharp corner in a type I functional response. For this new functional response, both models undergo Hopf, cyclic-fold, and Bautin bifurcations. We use our analyses to characterize predator–prey systems that may exhibit bistability.
Journal: Mathematical Biosciences - Volume 212, Issue 2, April 2008, Pages 161–179