Bifurcation Analysis of a Discrete-Time Two-Species Model
We study the local dynamics and bifurcation analysis of a discrete-time modified Nicholson–Bailey model in the closed first quadrant R+2. It is proved that model has two boundary equilibria: O0,0,Aζ1−1/ζ2,0, and a unique positive equilibrium Brer/er−1,r under certain parametric conditions. We study...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/2954059 |
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| Summary: | We study the local dynamics and bifurcation analysis of a discrete-time modified Nicholson–Bailey model in the closed first quadrant R+2. It is proved that model has two boundary equilibria: O0,0,Aζ1−1/ζ2,0, and a unique positive equilibrium Brer/er−1,r under certain parametric conditions. We study the local dynamics along their topological types by imposing method of Linearization. It is proved that fold bifurcation occurs about the boundary equilibria: O0,0,Aζ1−1/ζ2,0. It is also proved that model undergoes a Neimark–Sacker bifurcation in a small neighborhood of the unique positive equilibrium Brer/er−1,r and meanwhile stable invariant closed curve appears. From the viewpoint of biology, the stable closed curve corresponds to the period or quasi-periodic oscillations between host and parasitoid populations. Some simulations are presented to verify theoretical results. Finally, bifurcation diagrams and corresponding maximum Lyapunov exponents are presented for the under consideration model. |
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| ISSN: | 1026-0226 1607-887X |