A Three-Dimensional Chaotic System with Square Equilibrium and No-Equilibrium

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F17%3APU125271" target="_blank" >RIV/00216305:26220/17:PU125271 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/chapter/10.1007%2F978-3-319-50249-6_21" target="_blank" >https://link.springer.com/chapter/10.1007%2F978-3-319-50249-6_21</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-319-50249-6_21" target="_blank" >10.1007/978-3-319-50249-6_21</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A Three-Dimensional Chaotic System with Square Equilibrium and No-Equilibrium

Popis výsledku v původním jazyce

Recently, Leonov and Kuznetsov have introduced a new definition “hidden attractor”. Systems with hidden attractors, especially chaotic systems, have attracted significant attention. Some examples of such systems are systems with a line equilibrium, systems without equilibrium or systems with stable equilibria etc. In some interesting new research, systems in which equilibrium points are located on different special curves are reported. This chapter introduces a three-dimensional autonomous system with a square-shaped equilibrium and without equilibrium points. Therefore, such system belongs to a class of systems with hidden attractors. The fundamental dynamics properties of such system are studied through phase portraits, Poincaré map, bifurcation diagram, and Lyapunov exponents. Anti-synchronization scheme for our systems is proposed and confirmed by the Lyapunov stability. Moreover, an electronic circuit is implemented to show the feasibility of the mathematical model. Finally, we introduce the fractional order form of such system.

Název v anglickém jazyce

A Three-Dimensional Chaotic System with Square Equilibrium and No-Equilibrium

Popis výsledku anglicky

Recently, Leonov and Kuznetsov have introduced a new definition “hidden attractor”. Systems with hidden attractors, especially chaotic systems, have attracted significant attention. Some examples of such systems are systems with a line equilibrium, systems without equilibrium or systems with stable equilibria etc. In some interesting new research, systems in which equilibrium points are located on different special curves are reported. This chapter introduces a three-dimensional autonomous system with a square-shaped equilibrium and without equilibrium points. Therefore, such system belongs to a class of systems with hidden attractors. The fundamental dynamics properties of such system are studied through phase portraits, Poincaré map, bifurcation diagram, and Lyapunov exponents. Anti-synchronization scheme for our systems is proposed and confirmed by the Lyapunov stability. Moreover, an electronic circuit is implemented to show the feasibility of the mathematical model. Finally, we introduce the fractional order form of such system.

Druh

C - Kapitola v odborné knize

CEP obor

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OECD FORD obor

20201 - Electrical and electronic engineering

Projekt

<a href="/cs/project/GA15-22712S" target="_blank" >GA15-22712S: Chaotické chování subsystémů radiofrekvenčního kanálu</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název knihy nebo sborníku

Fractional Order Control and Synchronization of Chaotic Systems

ISBN

978-3-319-50249-6

Počet stran výsledku

22

Strana od-do

613-635

Počet stran knihy

877

Název nakladatele

Springer, Cham

Místo vydání

Neuveden

Kód UT WoS kapitoly

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