Existence and bifurcation of stable equilibrium in two-prey,one-predator communities |
| |
Authors: | Yasuhiro Takeuchi Norihiko Adachi |
| |
Affiliation: | (1) Department of Applied Mathematics, Faculty of Engineering, Shizuoka University, 432 Hamamatsu, Japan;(2) Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University, 606 Kyoto, Japan |
| |
Abstract: | In this paper, stability of two-prey, one-predator communities is investigated by Lyapunov's direct method and Hopf's bifurcation theory. Three patterns of three-species coexistence are possible. A globally stable non-negative equilibrium exists for the system even if two competing prey species without a predator cannot coexist. The stable equilibrium bifurcates to a periodic motion with a small amplitude when the predation rate increases. It is also shown that a chaotic motion emerges from the periodic motion when one of two prey has greater competitive abilities than the other. This predator-mediated coexistence can be realized by the intimate relationship between preferences of a predator and competitive abilities of two prey. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|