Stability and Hopf Bifurcation in Three-Dimensional Predator-Prey Models with Allee Effect
In thisstudy, we perform the stability and Hopf bifurcation analysis for twopopulation models with Allee effect. The population models within the scope ofthis study are the one prey-two predator model with Allee growth in the preyand the two prey-one predator model with Allee growth in the preys. Ou...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Sakarya University
2019-10-01
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| Series: | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/764622 |
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| Summary: | In thisstudy, we perform the stability and Hopf bifurcation analysis for twopopulation models with Allee effect. The population models within the scope ofthis study are the one prey-two predator model with Allee growth in the preyand the two prey-one predator model with Allee growth in the preys. Ourprocedure for investigating each model is as follows. First, we investigate thesingular points where the system is stable. We provide the necessary parameterconditions for the system to be stable at the singular points. Then, we lookfor Hopf bifurcation at each singular point where a family of limit cyclescycle or oscillate. We provide the parameter conditions for Hopf bifurcation tooccur. We apply the algebraic invariants method to fully examine the system. Weinvestigate the algebraic properties of the system by finding all algebraicinvariants of degree two and three. We give the conditions for the system tohave a first integral. |
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| ISSN: | 2147-835X |