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Singularity Structure and Chaotic Behavior of the Homopolar Disk Dynamo
Author(s) -
Sachdev P. L.,
Sarathy R.
Publication year - 1995
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 - 10.1002/sapm1995954345
Subject(s) - attractor , chaotic , dynamo , parametric statistics , singularity , bifurcation , mathematics , mathematical analysis , crisis , period doubling bifurcation , physics , classical mechanics , nonlinear system , statistical physics , computer science , magnetic field , statistics , quantum mechanics , artificial intelligence
We study in great detail a system of three first‐order ordinary differential equations describing a homopolar disk dynamo (HDD). This system displays a large variety of behaviors, both regular and chaotic. Existence of periodic solutions is proved for certain ranges of parameters. Stability criteria for periodic solutions are given. The nonintegrability aspects of the HDD system are studied by investigating analytically the singularity structure of the system in the complex domain. Coexisting attractors (including period‐doubling sequence) and coexisting strange attractors appear in some parametric regimes. The gluing of strange attractors and the ungluing of a strange attractor are also shown to occur. A period of bifurcation leading to chaos, not observed for other chaotic systems, is shown to characterize the chaotic behavior in some parametric ranges. The limiting case of the Lorenz system is also studied and is related to HDD.