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Hundreds of studies simulate the dynamics of local homogeneous populations and solve the problem of their optimal control. Dynamic conditions have been classified and scenarios of transitions from regular to chaotic behavior and vice versa have been studied for many specific populations to elaborate strategies for their optimal exploitation (Skaletskaya et al ., 1979;Abakumov, 1993;Furta, 1997;Holbauer and Sigmund, 1998). At the same time, the most valuable commercial species usually have a multiyear life cycle and complex age structure. This can be illustrated by sturgeons, whitefishes, and salmons of different industrial value. In addition, it can be hard to discriminate the dynamic changes induced by interpopulation mechanisms and anthropogenic influences in actively exploited populations. Mathematical simulations are the main approach in this situation; it allows us to study the effects of biotic and abiotic factors on the population dynamics separately. In this work, fishery-induced qualitative time-related changes were studied in a population with a complex age structure by the example of Pacific salmons. MATERIALS AND METHODSThe main target of this study is a population with an age structure and subject to fishing. The abundance is considered as the main index of population status. Similar to other living systems, population has the capacity for reproduction, growth, development, and exchange of energy and information between the environment and population components (individuals, age and sexual groups, etc.). However, a single model can hardly consider all interactions and properties intrinsic for the system studied. Mathematical modeling always involves certain generalization of both environment and simulated subject. In this case, we accept the following limitations:-the population is considered as isolated and no migrations are taken into account;-the lifecycle has a clear time periodicity related to the periodicity of the climate, which is manifested as alternation of more or less separate periods of reproduction and feeding; -for convenience, the period of time between two consecutive reproduction seasons is taken as one year;-continuity of survival is taken into account only in the first year of life (the survival coefficient is considered as a monotone decreasing function of the density); -the survival coefficients for individuals older than a year and fertility are considered independent of total population abundance;-environmental parameters are considered as constant.For convenience, we assume that fishing precedes the reproduction period in the process description. The amount of catch depends on current abundance and fishing efforts.The analytical study relied on classical approaches to the dynamics of recurrent systems, linear algebra, and mathematical analysis; while the numerical analysis involved the tools of the mathematical software package MathCAD. RESULTSSimulation of a homogeneous population . Let us first describe the changes in the abundance of a local population with seasonal reprod...

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