V. Amel'kin

Qualitative and Quantitative Characteristics of Limit Cycles

abstract:
In this article there are presented the criteria for existence, and there are also considered the questions of number, multiplicity and stability of limit cycles of the two-dimensional dynamic systems associated with a specific inversion of the Bendixson-Dulac criterion about the absence of closed trajectories in dynamic systems, and with the proposed by the author classification of limit cycles, based on the properties of the divergence of the vector field and the regularity conditions of cycles.

Mathematics Subject Classification: 34C05, 34C07.

Key words and phrases: Dynamic system, trajectory (of a dynamic system), limit cycle (of a dynamic system), divergence (of a vector field), stable (unstable, semistable) limit cycle, divergent limit cycle, rough (unrough) limit cycle, strict (nonstrict, generalized-strict) limit cycle, multiple (tuple) limit cycle, regular (non-regular) limit cycle, Poincaré function, topographical system of the curves, universal curvilinear-coordinate system.