Abstract
This paper concerns the analytical study of the general case of a new mathematical modelling on the γ-Ricker population models with a Holling type II per-capita birth function. The generalized Lambert W functions prove to be decisive in determining upper bounds for the number of fixed points of these models. In this approach, the use of the false derivative turns out to be very effective in solving generalized Lambert W functions of exponential polynomial and rational polynomial types, with multiple roots. The relation between the cusp points structures in the 4D parameter space considered and the variation of the number of fixed points is established.
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