Estimates for solutions in a model of reptile population dynamics

We consider a model of reptile population dynamics in which the gender of the future individuals depends on the environment temperature. The model is described by a system of delay differential equations in which the delay parameter is responsible for the time spent by individuals in immature age. We study the case of complete extinction of the entire population and the case of stabilization of the population size at a constant value. In each case Lyapunov-Krasovskii functionals are constructed, with the help of which we establish estimates characterizing the rate of extinction of the population in the first case and the rate of stabilization of the population size in the second. Using the obtained estimates, it is possible to evaluate the time for which the population size will reach the equilibrium state.