Premium
Singularity Structure of Third‐Order Dynamical Systems. II
Author(s) -
Sachdev P. L.,
Ramanan Sharadha
Publication year - 1997
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.00050
Subject(s) - singularity , mathematics , third order , transformation (genetics) , series (stratigraphy) , order (exchange) , mathematical analysis , convergence (economics) , type (biology) , polynomial , law , paleontology , biochemistry , chemistry , ecology , finance , biology , political science , economics , gene , economic growth
The singularity structure of the solutions of a general third‐order system, with polynomial right‐hand sides of degree less than or equal to two, is studied about a movable singular point. An algorithm for transforming the given third‐order system to a third‐order Briot–Bouquet system is presented. The dominant behavior of a solution of the given system near a movable singularity is used to construct a transformation that changes the given system directly to a third‐order Briot–Bouquet system. The results of Horn for the third‐order Briot–Bouquet system are exploited to give the complete form of the series solutions of the given third‐order system; convergence of these series in a deleted neighborhood of the singularity is ensured. This algorithm is used to study the singularity structure of the solutions of the Lorenz system, the Rikitake system, the three‐wave interaction problem, the Rabinovich system, the Lotka–Volterra system, and the May–Leonard system for different sets of parameter values. The proposed approach goes far beyond the ARS algorithm.