scholarly journals Periodic solutions and invariant torus in the Rössler system

Nonlinearity ◽  
2020 ◽  
Vol 33 (9) ◽  
pp. 4512-4539
Author(s):  
Murilo R Cândido ◽  
Douglas D Novaes ◽  
Claudia Valls
Keyword(s):  
Periodic Solutions ◽  
Invariant Torus ◽  
Rossler System ◽  
Rössler System

scholarly journals Differential Transform Method as an Effective Tool for Investigating Fractional Dynamical Systems

2021 ◽  
Vol 11 (15) ◽  
pp. 6955
Author(s):  
Andrzej Rysak ◽  
Magdalena Gregorczyk
Keyword(s):  
Optimal Parameter ◽  
Differential Transform Method ◽  
Bifurcation Diagrams ◽  
Transform Method ◽  
Rossler System ◽  
Differential Transform ◽  
Rössler System ◽  
Fractional System ◽  
Parameter Values

This study investigates the use of the differential transform method (DTM) for integrating the Rössler system of the fractional order. Preliminary studies of the integer-order Rössler system, with reference to other well-established integration methods, made it possible to assess the quality of the method and to determine optimal parameter values that should be used when integrating a system with different dynamic characteristics. Bifurcation diagrams obtained for the Rössler fractional system show that, compared to the RK4 scheme-based integration, the DTM results are more resistant to changes in the fractionality of the system.

A SIMPLE OBSERVER OF THE HYPERCHAOTIC RÖSSLER SYSTEM

2010 ◽  
Vol 24 (22) ◽  
pp. 4325-4331
Author(s):  
XING-YUAN WANG ◽  
JUN-MEI SONG
Keyword(s):  
Dynamical System ◽  
Time Domain ◽  
Global Exponential Stability ◽  
Observer Design ◽  
The Other ◽  
State Observation ◽  
Rossler System ◽  
Error System ◽  
Rössler System ◽  
The Time Domain

This paper studies the hyperchaotic Rössler system and the state observation problem of such a system being investigated. Based on the time-domain approach, a simple observer for the hyperchaotic Rössler system is proposed to guarantee the global exponential stability of the resulting error system. The scheme is easy to implement and different from the other observer design that it does not need to transmit all signals of the dynamical system. It is proved theoretically, and numerical simulations show the effectiveness of the scheme finally.

Adaptive Control of Chaotic Rössler System via Synchronization

2009 ◽  
Vol 4 (2) ◽  
pp. 98-106 ◽  
Author(s):  
H. Fatehi Marj ◽  
R. Asgharian ◽  
N. Pariz
Keyword(s):  
Adaptive Control ◽  
Rossler System ◽  
Rössler System

Chaos Synchronization of Hyperchaos Rossler System

2014 ◽  
Vol 687-691 ◽  
pp. 724-727
Author(s):  
Lin Wu ◽  
Jin Cheng Wei ◽  
Liu Jie
Keyword(s):  
Numerical Simulation ◽  
Chaos Synchronization ◽  
Simulation Experiment ◽  
Nonlinear Feedback ◽  
Driving System ◽  
Lyapunov Stabilization ◽  
Rossler System ◽  
Rössler System

Taking the hyperchaos Rossler system as an example and based on the Lyapunov Stabilization Law, with the parameters unknown, through the designing of controller, the synchronization of the driving system and the responding system has been realized by using the nonlinear feedback controlling method. This method provides a convenient way for the synchrocontrol of hyperchaos system, whose effectiveness has been further proved by the numerical simulation experiment.

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