Yalovega I. Nonlinear models of chemostat production of mixed cultures with interaction of commensalisms

The qualitative and quantitative analysis of two mathematical models of populations with interactions of competition and commensalisms in the throughput system is conducted in the thesis. This analysis gave the opportunity to solve the problem of control and to achieve optimal conditions of cultivation. The theory of differential equations and the theory of bifurcation are the basic methods of the investigation of such models. The mathematical model is offered as the system of the third order of the nonlinear differential equations, which describes production of mixed culture, consisting of two populations competing for the unique substrate with interactions of commensalisms, in the chemostat. All possible stationary states of two systems are found and examined for stability. Limitations of the growth characteristics and entering flows of the substrate and product are received. The analysis of the qualitative changes in the dynamics of investigating systems which were conditioned by variations of several parameters is conducted by means of the methods of bifurcation. The methods of the optimal control of the chemostat production have developed further.