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Two-Parameter Bifurcation in a Predator–Prey System of Ivlev Type

✍ Scribed by Jitsuro Sugie

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
195 KB
Volume
217
Category
Article
ISSN
0022-247X

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✦ Synopsis

Our concern is to consider an ecological system with Ivlev's functional response 1 y e ya x of predator to prey. In addition to a, this system contains parameters r and D, which represent the intrinsic rate of increase for the prey population and the death rate for the predator population, respectively. A necessary and sufficient condition for the uniqueness of limit cycles of the predator᎐prey system is Ž . presented. This result gives the bifurcation curve in the a, D -plane. ᮊ 1998 Academic Press Ž .

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Bifurcation analysis for a three-species
Bifurcation analysis for a three-species predator–prey system with two delays
✍ Maoxin Liao; Xianhua Tang; Changjin Xu 📂 Article 📅 2012 🏛 Elsevier Science 🌐 English ⚖ 520 KB

In this paper, a three-species predator-prey system with two delays is investigated. By choosing the sum s of two delays as a bifurcation parameter, we first show that Hopf bifurcation at the positive equilibrium of the system can occur as s crosses some critical values. Second, we obtain the formu