Ši'lnikov Chaos in the Generalized Lorenz Canonical Form of Dynamical Systems

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F05%3A03107464" target="_blank" >RIV/68407700:21230/05:03107464 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Ši'lnikov Chaos in the Generalized Lorenz Canonical Form of Dynamical Systems
Original language description
This paper studies the generalized Lorenz canonical form of dynamical systems introduced by Čelikovský and Chen [International Journal of Bifurcation and Chaos 12(8), 2002, 1789]. It proves the existence of a heteroclinic orbit of the canonical form andthe convergence of the corresponding series expansion. The Ši'lnikov criterion along with some technical conditions guarantee that the canonical form has Smale horseshoes and horseshoe chaos. As a consequence, it also proves that both the classical Lorenz system and the Chen system have Ši'lnikov chaos. When the system is changed into another ordinary differential equation through a nonsingular one-parameter linear transformation, the exact range of existence of Ši'lnikov chaos with respect to the parameter can be specified. Numerical simulation verifies the theoretical results and analysis.
Czech name
Šilnikovův chaos ve zobecněném Lorenzově systému
Czech description
Práce analyzuje Šilnikovův chaos ve zobecněném Lorenzově systému.

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BC - Theory and management systems
OECD FORD branch
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Project
<a href="/en/project/GA102%2F05%2F0011" target="_blank" >GA102/05/0011: Structure and Universality in Complex System Control Design</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2005
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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