scholarly journals Application of Piecewise Successive Linearization Method for the Solutions of the Chen Chaotic System

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
S. S. Motsa ◽  
Y. Khan ◽  
S. Shateyi
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Chaotic System ◽  
Good Accuracy ◽  
Linearization Method ◽  
Chen System ◽  
Successive Linearization Method ◽  
Runge Kutta

This paper centres on the application of the new piecewise successive linearization method (PSLM) in solving the chaotic and nonchaotic Chen system. Numerical simulations are presented graphically and comparison is made between the PSLM and Runge-Kutta-based methods. The work shows that the proposed method provides good accuracy and can be easily extended to other dynamical systems including those that are chaotic in nature.

A Chaotic System with Different Families of Hidden Attractors

2016 ◽  
Vol 26 (08) ◽  
pp. 1650139 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Christos Volos ◽  
Sajad Jafari ◽  
Sundarapandian Vaidyanathan ◽  
Tomasz Kapitaniak ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Chaotic System ◽  
Infinite Number ◽  
Mathematical Analysis ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Circuit Implementation ◽  
Hidden Attractors ◽  
Dynamical Behaviors

The presence of hidden attractors in dynamical systems has received considerable attention recently both in theory and applications. A novel three-dimensional autonomous chaotic system with hidden attractors is introduced in this paper. It is exciting that this chaotic system can exhibit two different families of hidden attractors: hidden attractors with an infinite number of equilibrium points and hidden attractors without equilibrium. Dynamical behaviors of such system are discovered through mathematical analysis, numerical simulations and circuit implementation.

Dissipative effects on a chemically and thermally radiative heat fluid flow past a shrinking porous sheet

2020 ◽  
pp. 1-14
Author(s):  
A. Shahid ◽  
M. Ali Abbas ◽  
H.L. Huang ◽  
S.R. Mishra ◽  
M.M. Bhatti
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Chemical Reaction ◽  
Linearization Method ◽  
Surface Drag ◽  
Suction Parameter ◽  
Similarity Transformations ◽  
Dissipative Effects ◽  
Successive Linearization Method

The present study analyses the dissipative influence into an unsteady electrically conducting fluid flow embedded in a pervious medium over a shrinkable sheet. The behavior of thermal radiation and chemical reactions are also contemplated. The governing partial differential equations are reformed to ordinary differential equations by operating similarity transformations. The numerical outcomes for the arising non-linear boundary value problem are determined by implementing the Successive linearization method (SLM) via Matlab software. The velocity, temperature, and concentration magnitudes for distant values of the governing parametric quantities are conferred, and their conduct is debated via graphical curves. The surface drag coefficient increases, whereas the local Nusselt number and Sherwood number decreases for enhancing unsteadiness parameter across suction parameter. Moreover, the magnetic and suction parameters accelerate velocity magnitudes while by raising porosity parameter, velocity decelerates. Larger numeric of thermal radiation parameter and Eckert number accelerates the temperature profile while by enhancing Prandtl number it decelerates. Schmidt number and chemical reaction parameters slowdowns the concentration distribution, and the chemical reaction parameter influences on the point of chemical reaction that benefits the interface mass transfer. It is expected that the current achieved results will furnish fruitful knowledge in industrious utilities.

scholarly journals Preface: Modelling and numerical simulations of dynamical systems

2017 ◽  
Vol 87 (5) ◽  
pp. 783-784
Author(s):  
Jan Awrejcewicz ◽  
Nuno Maia ◽  
Jerzy Mrozowski
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations

HYPERCHAOS IN THE FRACTIONAL-ORDER NONAUTONOMOUS CHEN'S SYSTEM AND ITS SYNCHRONIZATION

2005 ◽  
Vol 16 (05) ◽  
pp. 815-826 ◽  
Author(s):  
HONGBIN ZHANG ◽  
CHUNGUANG LI ◽  
GUANRONG CHEN ◽  
XING GAO
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic System ◽  
Three Dimensional ◽  
Synchronization Problem ◽  
Driving Signal

Recently, a new hyperchaos generator, obtained by controlling a three-dimensional autonomous chaotic system — Chen's system — with a periodic driving signal, has been found. In this letter, we formulate and study the hyperchaotic behaviors in the corresponding fractional-order hyperchaotic Chen's system. Through numerical simulations, we found that hyperchaos exists in the fractional-order hyperchaotic Chen's system with order less than 4. The lowest order we found to have hyperchaos in this system is 3.4. Finally, we study the synchronization problem of two fractional-order hyperchaotic Chen's systems.

Trailing Edge Filings and a Modified Stodola’s Slip Factor for Centrifugal Impeller

2015 ◽  
Author(s):  
Guang Xi ◽  
Huijing Zhao ◽  
Zhiheng Wang
Keyword(s):  
Numerical Simulations ◽  
Good Accuracy ◽  
Centrifugal Impeller ◽  
Pressure Side ◽  
Compressor Stage ◽  
Trailing Edge ◽  
Obvious Effect ◽  
Quantitative Calculation ◽  
Slip Factor ◽  
Stage Efficiency

The paper investigates the effect of trailing edge filing in the impeller on the performances of impeller and compressor stage. The 3D viscous numerical simulations are carried out under different positions, thicknesses and lengths of filing. The results show that, the filing on the trailing edge has an obvious effect on the pressure ratios of impeller and compressor stage. The trailing edge filing has little effect on the impeller efficiency while the filing on the pressure side is favorable to improving the stage efficiency. Then, through correcting the blade angles at the suction and pressure sides, considering the viscosity and 3D characteristics of the flow, a modified slip factor formula is proposed for the centrifugal impeller with a trailing edge filing. The validation to the proposed formula shows that the proposed formula can be used to predict the slip factors of different filing cases with a good accuracy. It can provide a theoretical guidance for the quantitative calculation when using the filing technology to improve the performance of centrifugal impeller as well as the stage.

The Stick Motion of a Harmonically Excited, Friction-Induced Oscillator on a Sinusoidally Traveling Surface

2006 ◽  
Author(s):  
Albert C. J. Luo ◽  
Brandon C. Gegg ◽  
Steve S. Suh
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Dry Friction ◽  
The Other ◽  
Linear Oscillator ◽  
Analytical Prediction ◽  
Nonlinear Friction ◽  
Friction Forces

In this paper, the methodology is presented through investigation of a periodically, forced linear oscillator with dry friction, resting on a traveling surface varying with time. The switching conditions for stick motions in non-smooth dynamical systems are obtained. From defined generic mappings, the corresponding criteria for the stick motions are presented through the force product conditions. The analytical prediction of the onset and vanishing of the stick motions is illustrated. Finally, numerical simulations of stick motions are carried out to verify the analytical prediction. The achieved force criteria can be applied to the other dynamical systems with nonlinear friction forces possessing a CO - discontinuity.

Periodic Motions in an Autonomous System With a Discontinuous Vector Field

2020 ◽  
Author(s):  
Siyu Guo ◽  
Albert C. J. Luo
Keyword(s):  
Vector Field ◽  
Dynamical Systems ◽  
Numerical Simulations ◽  
Autonomous System ◽  
Parameter Study ◽  
Spring Stiffness ◽  
Algebraic Equations ◽  
Periodic Motions ◽  
Mapping Structures ◽  
The Stability

Abstract In this paper, periodic motions in an autonomous system with a discontinuous vector field are discussed. The periodic motions are obtained by constructing a set of algebraic equations based on motion mapping structures. The stability of periodic motions is investigated through eigenvalue analysis. The grazing bifurcations are presented by varying the spring stiffness. Once the grazing bifurcation occurs, periodic motions switches from the old motion to a new one. Numerical simulations are conducted for motion illustrations. The parameter study helps one understand autonomous discontinuous dynamical systems.

Jacobi analysis for an unusual 3D autonomous system

2020 ◽  
Vol 17 (04) ◽  
pp. 2050062 ◽  
Author(s):  
Chunsheng Feng ◽  
Qiujian Huang ◽  
Yongjian Liu
Keyword(s):  
Chaotic System ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Chen System ◽  
Parameter Region ◽  
Stable Equilibria ◽  
The Lorenz System ◽  
Deviation Vector

Little seems to be known about the study of the chaotic system with only Lyapunov stable equilibria from the perspective of differential geometry. Therefore, this paper presents Jacobi analysis of an unusual three-dimensional (3D) autonomous chaotic system. Under certain parameter conditions, this system has positive Lyapunov exponents and only two linear stable equilibrium points, which means that chaotic attractor and Lyapunov stable equilibria coexist. The dynamical behavior of the deviation vector near the whole trajectories (including all equilibrium points) is analyzed in detail. The results show that the value of the deviation curvature tensor at equilibrium points is only related to parameters; the two equilibrium points of the system are Jacobi stable if the parameters satisfy certain conditions. Particularly, for a specific set of parameters, the linear stable equilibrium points of the system are always Jacobi unstable. A periodic orbit that is Lyapunov stable is also proven to be always Jacobi unstable. Next, Jacobi-stable regions of the Lorenz system, the Chen system and the system under study are compared for specific parameters. It can be found that although these three chaotic systems are very similar, their regions of Jacobi stable parameters are much different. Finally, by comparing Jacobi stability with Lyapunov stability, the obtained results demonstrate that the Jacobi stable parameter region is basically symmetric with the Lyapunov stable parameter region.

scholarly journals Some Problems of Feedback Control Strategies and It’s Treatment

2017 ◽  
Vol 9 (1) ◽  
pp. 39 ◽  
Author(s):  
Maysoon M. Aziz ◽  
Saad Fawzi AL-Azzawi
Keyword(s):  
Dynamical Systems ◽  
Feedback Control ◽  
Numerical Simulations ◽  
Positive Feedback ◽  
Control Strategies ◽  
Novel Approach

This paper extends and improves the feedback control strategies. In detailed, the ordinary feedback, dislocated feedback, speed feedback and enhancing feedback control for a several dynamical systems are discussed here. It is noticed that there some problems by these strategies. For this reason, this Letter proposes a novel approach for treating these problems. The results obtained in this paper show that the strategies with positive feedback coefficients can be controlled in two cases and failed in another two cases. Theoretical and numerical simulations are given to illustrate and verify the results.

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