Investigation of the dynamical properties of a fourth-oder system with one limiting point by the root-trajectory method

The family of root trajectories of a fourth-order system with the characteristic equation(a$_0$p$^{4}$+a$_1$p$^3$+a$_2$p$^2$+a$_3$p+a$_4$+K(b$_0$p+b$_1$)=0 is investigated. Having determined the types of root trajectory, their analysis leads to the establishment of general properties, allowing calculations of such systems to be more expediently performed.