Hyperchaos in the Fractional-Order Lü System and its Synchronization

2014 ◽  
Vol 905 ◽  
pp. 464-468 ◽  
Author(s):  
Tian Zeng Li ◽  
Yu Wang
Keyword(s):  
Numerical Simulation ◽  
Fractional Order ◽  
Control Parameter ◽  
Coupling Method ◽  
Lü System ◽  
Simulation Results ◽  
The One ◽  
Lu System

The hyperchaotic behaviors in the fractional hyperchaotic Lü system are studied. And we give the lowest orders for generating hyperchaos with different control parameter. Hyperchaos synchronization of Lü system is theoretically and numerically studied using the one-way coupling method. The numerical simulation results demonstrate the effectiveness and validity of the method.

Anti-Synchronization Control of the Complex Lu System

2014 ◽  
Vol 721 ◽  
pp. 269-272
Author(s):  
Fan Di Zhang
Keyword(s):  
Complex System ◽  
Fractional Order ◽  
Control Strategy ◽  
Stability Theorem ◽  
Projective Synchronization ◽  
Synchronization Control ◽  
Fractional Order Systems ◽  
Lü System ◽  
The Stability ◽  
Lu System

This paper propose fractional-order Lu complex system. Moreover, projective synchronization control of the fractional-order hyper-chaotic complex Lu system is studied based on feedback technique and the stability theorem of fractional-order systems, the scheme of anti-synchronization for the fractional-order hyper-chaotic complex Lu system is presented. Numerical simulations on examples are presented to show the effectiveness of the proposed control strategy.

A New Five Dimensional Hyperchaotic System and its Fractional Order Form

2013 ◽  
Vol 464 ◽  
pp. 375-380 ◽  
Author(s):  
Ling Liu ◽  
Chong Xin Liu ◽  
Yi Fan Liao
Keyword(s):  
Numerical Simulation ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Simulation Analysis ◽  
Three Dimensional ◽  
Hyperchaotic System ◽  
Order Form ◽  
Simulation Results ◽  
Predictor Corrector ◽  
New Hyperchaotic System

In this paper, a new five-dimensional hyperchaotic system by introducing two additional states feedback into a three-dimensional smooth chaotic system. With three nonlinearities, this system has more than one positive Lyapunov exponents. Based on the fractional derivative theory, the fractional-order form of this new hyperchaotic system has been investigated. Through predictor-corrector algorithm, the system is proved by numerical simulation analysis. Simulation results are provided to illustrate the performance of the fractional-order hyperchaotic attractors well.

Pollutant Transport Model and Numerical Simulation in Landfill Site

2012 ◽  
Vol 443-444 ◽  
pp. 424-429
Author(s):  
Ying Zhao ◽  
Qiang Xue ◽  
Lei Liu ◽  
Bing Liang
Keyword(s):  
Numerical Simulation ◽  
Control System ◽  
Simulation Model ◽  
Landfill Leachate ◽  
Transport Model ◽  
Control Measure ◽  
Underground Water ◽  
Seepage Control ◽  
Simulation Results ◽  
The One

The simulation model for describing the transportation and transformation of landfill leachate pollutant in landfill, soil and underground water was established. Taking Wuhan Changshankou landfill for example, the numerical simulation was carried out. The simulation results showed that if there’s no any seepage control measure, the groundwater and soil under landfill will be polluted seriously after MSW was filled; the highest pollutant concetration in landfill was about 25000, and the one in groundwater and soil was about 20000; at the thirtieth year, the pollutant concetration in groundwater and soil still remained up to 10000 although the one in landfill was about 0. The simulation results also showed that the vertical stonewall can’t be used as a nature, and artificial seepage control system must be used.

Estimation of the Order and Parameters of a Fractional Order Model From a Noisy Step Response Data1

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Mahsan Tavakoli-Kakhki ◽  
Mohammad Saleh Tavazoei
Keyword(s):  
Numerical Simulation ◽  
Fractional Order ◽  
Closed Loop ◽  
Open Loop ◽  
Measurement Noise ◽  
Step Response ◽  
Order Model ◽  
Response Data ◽  
Fractional Order Model ◽  
Simulation Results

This paper deals with integral based methods to estimate the order and parameters of simple fractional order models from the extracted noisy step response data of a process. This data can be obtained from both open-loop and closed-loop tests. Numerical simulation results are presented to verify the robustness of these proposed methods in the presence of the measurement noise.

scholarly journals Investigation of Chaotic and Strange Nonchaotic Phenomena in Nonautonomous Wien-Bridge Oscillator with Diode Nonlinearity

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
R. Rizwana ◽  
I. Raja Mohamed
Keyword(s):  
Numerical Simulation ◽  
Mean Square Displacement ◽  
Dynamical Variable ◽  
Mean Square ◽  
Maximal Lyapunov Exponent ◽  
Simulation Results ◽  
The One ◽  
Nonlinear Behaviors ◽  
Bifurcation Process ◽  
Electronic Oscillator

We have studied the chaotic and strange nonchaotic phenomena of a simple quasiperiodically forced Wien bridge oscillator circuit with diode as the only nonlinearity in this electronic oscillator system responsible for various nonlinear behaviors. Both the experimental results and the numerical simulation results for their confirmation are provided to show the bifurcation process. Various measures used for the numerical confirmation of SNA are power spectrum, maximal Lyapunov exponent, path of translational variables, mean square displacement, projection of poincaré section, log-log plot, and autocorrelation function. Based upon the numerical results, the birth of SNAs has been identified in the band merging route, intermittency route, and blowout bifurcation route. In addition, the birth of SNAs has been analyzed with peculiar mechanism, namely, “0-1 Test” employing the one state dynamical variable.

Bivariate Module-Phase Synchronization of a Fractional-Order Lorenz System in Different Dimensions

2013 ◽  
Vol 8 (3) ◽  
Author(s):  
Xing-Yuan Wang ◽  
Hao Zhang
Keyword(s):  
Numerical Simulation ◽  
Phase Space ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Lorenz System ◽  
Phase Synchronization ◽  
High Dimensional ◽  
Different Dimensions ◽  
Simulation Results ◽  
First Time

Based on the classic Lorenz system, this paper studies the problem of bivariate module-phase synchronizations in a fractional-order Lorenz system, bivariate module-phase synchronizations in a fractional-order spatiotemporal coupled Lorenz system, and malposed module-phase synchronization in a fractional-order spatiotemporal coupled Lorenz system. It is the first time, to our knowledge, that module-phase synchronization in fractional-order high-dimensional systems is applied. According to the fractional calculus techniques and spatiotemporal theory, we design controllers and achieve synchronizations both in module space and phase space at the same time. In the simulation, we discuss the bivariate module-phase synchronization and malposed module-phase synchronization. The numerical simulation results demonstrate the validity of controllers.

Numerical Simulation in Rear Axlecap of Automobile Drawing Process and Optimization of Technological Parameters

2010 ◽  
Vol 148-149 ◽  
pp. 1171-1176
Author(s):  
Ju Hua Huang ◽  
Li Xian Li ◽  
Ying Ying Wan ◽  
Jun Tuan Guo
Keyword(s):  
Numerical Simulation ◽  
Rear Axle ◽  
Element Model ◽  
Drawing Process ◽  
Work Efficiency ◽  
Technological Parameters ◽  
Simulation Results ◽  
Quality Of Products ◽  
The One

This paper takes the rear axle cap which is a typical automobile covering part as the research object. 3D and finite element model of it are built, and the drawing process is simulated with Dynaform, then the technological parameters are analyzed and optimized based on the simulation results, finally the part is compared with the one that is processed in practice. The results show that this method is easy and feasible, it not only increase the work efficiency greatly but also improve the quality of products.

scholarly journals A New Synchronization Method for Time-Delay Fractional Complex Chaotic System and Its Application

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3305
Author(s):  
Junmei Guo ◽  
Chunrui Ma ◽  
Xinheng Wang ◽  
Fangfang Zhang ◽  
Michaël Antonie van Wyk ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Time Delay ◽  
Secure Communication ◽  
Speech Communication ◽  
Lü System ◽  
Adomian Decomposition ◽  
Speech Transmission ◽  
Definition Of ◽  
Lu System ◽  
Function Synchronization

This paper proposes a class of time-delay fractional complex Lu¨ system and utilizes the adomian decomposition algorithm to study the dynamics of the system. Firstly, the time chaotic attractor, coexistence attractor and parameter space are studied. The bifurcation diagram and complexity are used to analyze the dynamic characteristics of the system. Secondly, the definition of modified fractional projective difference function synchronization (MFPDFS) is introduced. The corresponding synchronous controller is designed to realize the MFPDFS of the time-delay fractional complex Lu¨ system. Thirdly, based on the background of wireless speech communication system (WSCs), the MFPDFS controller is used to realize the secure speech transmission. Finally, the effectiveness of the controller is verified by numerical simulation. The signal-noise ratio (SNR) analysis of speech transmission is given. The performance of secure communication is verified by numerical simulation.

Integer and Fractional Order Multiwing Chaotic Attractors via the Chen System and the Lü System with Switching Controls

2014 ◽  
Vol 24 (03) ◽  
pp. 1450029 ◽  
Author(s):  
Fei Xu
Keyword(s):  
Fractional Order ◽  
Control Strategies ◽  
Chaotic Attractors ◽  
Chen System ◽  
Lü System ◽  
System A ◽  
Controlled Systems ◽  
Dynamical Behaviors ◽  
Linear Differential ◽  
Lu System

In this work, we investigate the generation of multiwing chaotic attractors using integer and fractional order linear differential equation systems with switching controls. Based on the properties of the Chen system and the Lü system, a series of switching control strategies are proposed to link two linearized, integer or fractional order such systems. Numerical simulation results indicate that the controlled systems exhibit a variety of rich dynamical behaviors including multiwing and grid multiwing chaotic attractors.

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