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Singularity Structure of Third‐Order Dynamical Systems. I
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 - 10.1111/1467-9590.00049
Subject(s) - singularity , third order , mathematics , laurent series , transformation (genetics) , order (exchange) , series (stratigraphy) , dynamical systems theory , singular point of a curve , dynamical system (definition) , polynomial , mathematical analysis , physics , law , paleontology , biochemistry , chemistry , finance , quantum mechanics , biology , political science , economics , gene
A general third‐order dynamical system with polynomial right‐hand sides of finite degrees in the dependent variables is analyzed to unravel the singularity structure of its solutions about a movable singular point. To that end, the system is first transformed to a second‐order Briot–Bouquet system and a third auxiliary equation via a transformation, similar to one used earlier by R. A. Smith in 1973–1974 for a general second‐order dynamical system. This transformation imposes some constraints on the coefficients appearing in the general third‐order system. The known results for the second‐order Briot–Bouquet system are used to explicitly write out Laurent or psi‐series solutions of the general third‐order system about a movable singularity. The convergence of the relevant series solutions in a deleted neighborhood of the singularity is ensured. The theory developed here is illustrated with the help of the May–Leonard system.