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

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

• γ-Ricker population model
• Lambert <i>W</i> function
• Allee effect
• fixed point
• fold and flip bifurcations