Bifurcation phenomena and processes in the flow formed in a three-dimensional phase space by a dynamic system with square-law nonlinearity

Autor:	S. N. Vladimirov, V. A. Borodin, M. S. Zinkevich
Rok vydání:	2006
Předmět:	Nonlinear Sciences::Chaotic Dynamics Physics Period-doubling bifurcation Transcritical bifurcation Pitchfork bifurcation Law General Physics and Astronomy Feigenbaum constants Bogdanov–Takens bifurcation Saddle-node bifurcation Infinite-period bifurcation Bifurcation diagram
Zdroj:	Russian Physics Journal. 49:987-996
ISSN:	1573-9228 1064-8887
DOI:	10.1007/s11182-006-0214-6
Popis:	The basic laws of operation of a dynamic system with square-law nonlinearity and three-dimensional phase space are studied analytically, numerically, and experimentally. Results of analytical investigations of the stability of special points in the system and of numerical and full-scale experiments that indicate the existence of a sequence of bifurcation phenomena described by the Feigenbaum scenario are presented. The existence of two critical values of the control parameter, the first of which characterizes the first Hopf bifurcation and the second describes the destruction of motion at the expense of confluence of the chaotic attractor with the vicinity of the special repeller-type point, is proved.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::532f28968f43f7c0278e01d706ad2545 https://doi.org/10.1007/s11182-006-0214-6 Zobrazit plný text záznamu Plný text ve formátu PDF