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Efim Frisman, Oksana Revutskaya, Galina Neverova
In this paper, we investigate a discrete model of population dynamics for the species with simple age structure. The cases when survival rates represent the functions of both age groups numbers are considered. We classify the types of dynamical modes and investigate the scenario of transition from regular to chaotic behavior, and vice versa. The optimization problem is stated and investigated. The problem was to find optimum catch quotas and a steady value of population number providing a theoretically maximum possible sustainable yield. It is shown that a single age class harvesting is the optimal one, and a choice of the age class is determined by the values of population parameters and prices ratio. It is found that stationary harvesting strategy with constant quota stabilizes the population dynamics for definite values of parameters. However, there is a range of the parameters at which there appear two-year fluctuations of number in the population. It leads to the necessity of transfer from harvesting based on constant catch quotas to threshold harvesting. It is shown that the threshold strategy always stabilizes the system’s dynamics.
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