Automatic analysis of D-partition

[摘要] The paper is dedicated to automatization of D-partition analysis. D-partition is one of the most common methods for determination of solution stability in systems with time-delayed feedback control and its dependency on values of control parameters. A transition from analytical form of D-partition to plain graph has been investigated. An algorithm of graph faces determination and calculation of count of characteristic equation roots with positive real part for appropriate area of D-partition has been developed. The algorithm keeps an information about analytical formulas for edges of faces. It allows to make further analytical research based on the results of computer analysis.

[发布机构] Yaroslavl State University, Yaroslavl, Russia^1

[效力级别] 数学

[关键词] Analytical formulas;Analytical research;Automatic analysis;Characteristic equation;Computer analysis;Control parameters;Solution stability;Time delayed feedback control