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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 and the 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.
- 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 and the 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. (en)
- Práce analyzuje Šilnikovův chaos ve zobecněném Lorenzově systému. (cs)
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Title
| - Ši'lnikov Chaos in the Generalized Lorenz Canonical Form of Dynamical Systems
- Šilnikovův chaos ve zobecněném Lorenzově systému (cs)
- Ši'lnikov Chaos in the Generalized Lorenz Canonical Form of Dynamical Systems (en)
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skos:prefLabel
| - Ši'lnikov Chaos in the Generalized Lorenz Canonical Form of Dynamical Systems
- Šilnikovův chaos ve zobecněném Lorenzově systému (cs)
- Ši'lnikov Chaos in the Generalized Lorenz Canonical Form of Dynamical Systems (en)
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skos:notation
| - RIV/68407700:21230/05:03107464!RIV08-GA0-21230___
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http://linked.open.../vavai/riv/strany
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http://linked.open...avai/riv/aktivita
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http://linked.open...avai/riv/aktivity
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http://linked.open...iv/cisloPeriodika
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http://linked.open...vai/riv/dodaniDat
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http://linked.open...aciTvurceVysledku
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http://linked.open.../riv/druhVysledku
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http://linked.open...iv/duvernostUdaju
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http://linked.open...titaPredkladatele
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http://linked.open...dnocenehoVysledku
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http://linked.open...ai/riv/idVysledku
| - RIV/68407700:21230/05:03107464
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http://linked.open...riv/jazykVysledku
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http://linked.open.../riv/klicovaSlova
| - generalized Lorenz canonical form; heteroclinic orbit; Ši'lnikov criterion (en)
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http://linked.open.../riv/klicoveSlovo
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http://linked.open...odStatuVydavatele
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http://linked.open...ontrolniKodProRIV
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http://linked.open...i/riv/nazevZdroje
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http://linked.open...in/vavai/riv/obor
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http://linked.open...ichTvurcuVysledku
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http://linked.open...cetTvurcuVysledku
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http://linked.open...vavai/riv/projekt
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http://linked.open...UplatneniVysledku
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http://linked.open...v/svazekPeriodika
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http://linked.open...iv/tvurceVysledku
| - Čelikovský, Sergej
- Chen, G.
- Zhou, T.
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http://localhost/t...ganizacniJednotka
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