Applied Mathematics & Information Sciences

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In this paper, a model of predator-two preys system dynamics is considered. Within the framework of such model, it is assumed that preys are not competitors. The hypothesis that the simultaneous existence of three species excluding realization of regimes of mass propagation is tested. It is believed that elimination of one of prey populations leads to conditions when other population obtains the opportunity to escape from predator’s control and to realize mass propagation. In this model, a nonlinear control law is taken into account. This variant of system management allows provision of effective control of population sizes. In particular, this control mechanism does not allow phytophagous escaping out of control of their enemies, and prey population sizes stabilize at lower values than it was observed before using control law. Thus, there is a principal possibility of organizing prey population sizes control by release of additional preys into the system and the control influence.

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