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

被引：0

作者：

Rocha, J. Leonel ^{[1
,2
]}

Taha, Abdel-Kaddous ^{[3
]}

Abreu, Stella ^{[4
]}

机构：

[1] Polytech Inst Lisbon, CEAUL, Rua Conselheiro Emidio Navarro 1, P-1959007 Lisbon, Portugal

[2] Polytech Inst Lisbon, ISEL Engn Super Inst Lisbon, Dept Math, Rua Conselheiro Emidio Navarro 1, P-1959007 Lisbon, Portugal

[3] Fed Univ Toulouse Midi Pyrenees, INSA, 135 Ave Rangueil, F-31077 Toulouse, France

[4] Polytech Porto, CMUP, LEMA, ISEP, Rua Dr Antonio Bernardino Almeida 431, P-4249015 Porto, Portugal

来源：

MATHEMATICS | 2024年 / 12卷 / 12期

关键词：

gamma-Ricker population model; Lambert W function; Allee effect; fixed point; fold and flip bifurcations;

D O I：

10.3390/math12121805

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 gamma-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 gamma is even or odd. In addition, the analysis of the bifurcation structure of this gamma-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.

引用

页数：25