TITLE:
On the Asymptotic Stability of Discrete Crocodilians Model
AUTHORS:
Kaori Saito, Yoshihiro Hamaya
KEYWORDS:
Asymptotic Stability, Crocodilians Population Model, Positive Equilibrium Point
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.13 No.5,
May
11,
2023
ABSTRACT: The sex ratio of crocodiles is strongly biased towards females, often as high as 10 females to 1 male. In crocodilians, the temperature of egg incubation is the environmental factor determining sex. If the temperature is low, around 30˚C, the hatchlings are all females. Higher temperature, around 34˚C, hatch all males. This study was made to consider the asymptotic stability of a positive equilibrium point in a nonlinear discrete model of the basic nesting population model, which is described in three-region depending on the temperature of egg incubation. This model is based on key life-historical data and Murray’s research. To study above, we have applied the classical linearization method and P. Cull’s method and moreover, we employ non-standard discretization methods for later our Equations (6)-(8) and (15).