Complexity-stability relationship of two-prey-one-predator species system model: Local and global stability |
| |
Authors: | Koichi Fujii |
| |
Institution: | Department of Biological Sciences, Purdue University, West Lafayette, IN 47907 U.S.A. |
| |
Abstract: | Parrish & Saila (1970), motivated by the experiments of Paine (1966), constructed a simple mathematical model for a two-prey-one-predator system. They were unable to find, in their model, a set of parametric values with which the three-species system can be stable, whereas a twoprey species system without a predator is unstable. Cramer & May (1972) showed that, in fact, such parametric values exist, and gave the necessary mathematical condition. I have investigated the complete conditions for the stability of the system around the equilibrium point, and show that the conditions must be more stringent than given by Cramer & May (1972). Also, it is shown that the present model can have a globally stable limit cycle in three species even when the equilibrium point is locally unstable. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|