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The paper investigates influence of sex- and age-specific harvest on the dynamics of structured populations based on the mathematical model with discrete time. We assume birth rate depends on the population sex ratio and is described by the modified harmonic mating function with switching. The population size is regulated by decreasing juvenile survival rate with growth of sex-age class sizes. The aim is to study the mechanisms of formation and evolution of dynamic modes for the exploited structured population models due to harvesting intensity. Conditions for sustainable development of the exploited population are received. Dynamic modes of the population models are studied. Influence of birth, survival, and self-regulation rates, the formation process of the mating pairs, and sex- and age-specific harvest on transitions between different dynamic modes are investigated. Sex-specific harvest of mature females or males will change the pair formation if the sex class, whose number of individuals is more, is exploited. Depending on values of the population parameters, the sex- and age-specific harvest (juveniles, mature females or males) can result in both damping of the oscillations, which stabilizes population dynamics, and the oscillation appearance, including two-year or quasiperiodic population fluctuations. The model of exploited population reveals the phenomenon of multistability, which is typical for a population without harvesting. The multistability is the result of complex bifurcations occurring due to both the system nonlinearity and the changing pair formation principle.

Using a mathematical model of the number dynamics in a population with age and sex structure, the relationships were studied between the number of newborns and that of mature females and males. In addition, we studied transitions between different modes of population dynamics which were dependent on changes in not only the population parameters, such as reproduction intensity, survival, and self-regulation, but also in mating pair formation. Population dynamics was found to manifest multistability; i.e., the alternative dynamics modes were observed at the same values of the population parameters but under different initial conditions.

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