Dynamic systems in a broad sense may be considered as mathematical models of processes and phenomena, where any statistical events we may disregard. The dynamic systems theory investigates curves, defined by differential equations. The same time the laws of Nature are written using the language of differential equations, as the great French mathematician and encyclopedist of the nineteenth and twentieth centuries J.H. Poincare has taught. Thus, these laws are written using dynamic systems. A study of a given family of dynamic systems depending on several parameters means splitting of a phase space belonging to the dynamic system under consideration into trajectories and investigation of the limit behavior of them with the aim to reveal and describe their positions of equilibrium, and to find the so-called sinks and sources. Also, very important are the question of the stability of equilibrium states and their types, as well as the question of a roughness of a system. Rough dynamic systems can preserve their qualitative character of motion under some considerably small changes in parameters of the system. The paper is devoted to the original investigation of a broad family of polynomial dynamic systems, depending on multiple parameters.
Dynamic systems, Trajectories, Phase portraits, Equilibrium states, Differential equations, Poincare sphere, Poincare disk, Singular points, Separatrices, Limit cycles