Three-Phase Dynamical Systems and Their Applications to Monitoring for the Development of Hydrocarbon Fields

The behavior and properties of solutions to three-phase quadratic polynomial dynamical systems on the phase plane of variables and time are considered. A complete qualitative theory is constructed which includes the analysis of all singular points and the properties of solutions depending on all parameters of the problem. Integrability in elementary functions is proved for a class of autonomous polynomial dynamical systems. With the discriminant criteria created on the basis of the constructed model, it is shown that one can identify all stable and unstable solutions and formulate practical recommendations for regulating the regimes of wells and monitoring and optimization for the development of oil and gas fields.