Qualitative Theory of Two-Dimensional Polynomial Dynamical Systems

A qualitative theory of two-dimensional quadratic-polynomial integrable dynamical systems (DSs) is constructed on the basis a discriminant criterion elaborated in paper. This enables one to pick up single parameter that makes it possible identify all feasible solution classes as well DS critical and singular points solutions. The integrability considered family established. Nine specific are identified. In each class, clear types symmetry determined visualized discussed how transformations between create new symmetries. Visualization performed series phase portraits revealing catastrophic scenarios result from transition classes.