Generalized r-Lambert function in the analysis of fixed points and bifurcations of homographic 2-Ricker maps
This paper aims to study the nonlinear dynamics and bifurcation structures of a new mathematical model of the γ-Ricker population model with a Holling type II per-capita birth function, where the Allee effect parameter is γ = 2. A generalized r-Lambert function is defined on the 3D parameters space...
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| Format: | article |
| Language: | eng |
| Published: |
2021
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| Online Access: | http://hdl.handle.net/10400.21/13781 |
| Country: | Portugal |
| Oai: | oai:repositorio.ipl.pt:10400.21/13781 |
| Summary: | This paper aims to study the nonlinear dynamics and bifurcation structures of a new mathematical model of the γ-Ricker population model with a Holling type II per-capita birth function, where the Allee effect parameter is γ = 2. A generalized r-Lambert function is defined on the 3D parameters space to determine the existence and variation of the number of nonzero fixed points of the homographic 2-Ricker maps considered. The singularity points of the generalized r-Lambert function are identified with the cusp points on a fold bifurcation of the homographic 2-Ricker maps. In this approach, the application of the transcendental generalized r-Lambert function is demonstrated based on the analysis of local and global bifurcation structures of this three-parameter family of homographic maps. Some numerical studies are included to illustrate the theoretical results. |
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