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Advisor(s)
Abstract(s)
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.
Description
Keywords
γ-Ricker population model Generalized r-Lambert function Fixed point Fold and flip bifurcations Cusp point
Citation
ROCHA, J. Leonel; TAHA, Abdel-Kaddous – Generalized r-Lambert function in the analysis of fixed points and bifurcations of homographic 2-Ricker maps. International Journal of Bifurcation and Chaos. ISSN 0218-1274. Vol. 31, N.º 11 (2021), pp. 2130033-1- 2130033-19
Publisher
World Scientific Publishing Company