The mathematical model of the number dynamic for the homogeneous exploited population and analysis of the trade influence on the dynamic character

In this work were analyzed the contradictions between the strategy of the optimum withdrawal and population stability. As an example we have used the homogeneous population with periodical reproduction (the mathematical model with discrete time). The annual withdrawal was formalized through the exploitation intensity (trade effort amount) depending on the of the exploited population level.
The optimum strategy of the withdrawal is intended to achieve the maximal yield while preserving the stable population level. We have shown, that the equilibrium population stock remains stable when exploitation intensity is constant and can become unstable at variable intensity. Thus, it was shown that the exploitation with the variable ratio of withdrawal can cause the fluctuation of population stock, or force transition of the population to the new stationary level, which frequently means the degeneration of the population.