Lambert W Functions in the Analysis of Nonlinear Dynamics and Bifurcations of a 2D γ -Ricker Population Model

J. Leonel Rocha (), Abdel-Kaddous Taha and Stella Abreu
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J. Leonel Rocha: CEAUL and Department of Mathematics of ISEL-Engineering Superior Institute of Lisbon, Polytechnic Institute of Lisbon, Rua Conselheiro Emídio Navarro 1, 1959-007 Lisboa, Portugal
Abdel-Kaddous Taha: INSA, Federal University of Toulouse Midi-Pyrénées, 135 Avenue de Rangueil, 31077 Toulouse, France
Stella Abreu: CMUP, LEMA, ISEP, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida 431, 4249-015 Porto, Portugal

Mathematics, 2024, vol. 12, issue 12, 1-25

Abstract: The aim of this paper is to study the use of Lambert W functions in the analysis of nonlinear dynamics and bifurcations of a new two-dimensional γ -Ricker population model. Through the use of such transcendental functions, it is possible to study the fixed points and the respective eigenvalues of this exponential diffeomorphism as analytical expressions. Consequently, the maximum number of fixed points is proved, depending on whether the Allee effect parameter γ is even or odd. In addition, the analysis of the bifurcation structure of this γ -Ricker diffeomorphism, also taking into account the parity of the Allee effect parameter, demonstrates the results established using the Lambert W functions. Numerical studies are included to illustrate the theoretical results.

Keywords: ?-Ricker population model; Lambert W function; Allee effect; fixed point; fold and flip bifurcations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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