Field methods of investigation of nonlinear dynamic systems. II (Q912824)

The paper represents the second part [for part I see Autom. Remote Control 48, No.6, 714-722 (1987); transl. from Avtom. Telemekh. 1987, No.6, 7-18 (1987; Zbl 0651.93058)] of a notable contribution in the study of nonlinear dynamic systems described by a set of ordinary differential equations of the form \(\dot x=f(x,t)\), \(x\in X={\mathbb{R}}^ n.\) Using the concept of drift (which represents a supplementary condition for \(x_ k(t,x_ 0,t_ 0))\) the author establishes a set of criteria for stability and instability of the equilibrium point (especially in terms of the right-hand side f(x,t)). Some illustrative examples and a discussion about the cusps (also with reference to the drift concept) permit to compare these new methods with others existing in the literature.