scholarly journals Hyperchaos Numerical Simulation and Control in a 4D Hyperchaotic System

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Junhai Ma ◽  
Yujing Yang
Keyword(s):  
Lyapunov Exponents ◽  
Equilibrium Points ◽  
Linear Feedback ◽  
Hyperchaotic System ◽  
Bifurcation Diagrams ◽  
Theory Analysis ◽  
Feedback Controllers ◽  
Dynamic Simulations ◽  
Wide Range ◽  
And Control

A hyperchaotic system is introduced, and the complex dynamical behaviors of such system are investigated by means of numerical simulations. The bifurcation diagrams, Lyapunov exponents, hyperchaotic attractors, the power spectrums, and time charts are mapped out through the theory analysis and dynamic simulations. The chaotic and hyper-chaotic attractors exist and alter over a wide range of parameters according to the variety of Lyapunov exponents and bifurcation diagrams. Furthermore, linear feedback controllers are designed for stabilizing the hyperchaos to the unstable equilibrium points; thus, we achieve the goal of a second control which is more useful in application.

scholarly journals Dynamical behavior and control of a new hyperchaotic Hamiltonian system

2021 ◽  
Vol 7 (4) ◽  
pp. 5117-5132
Author(s):  
Junhong Li ◽  
◽  
Ning Cui
Keyword(s):  
Hamiltonian System ◽  
Nonholonomic Constraint ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Linear Feedback ◽  
Hyperchaotic System ◽  
Linear Feedback Control ◽  
Dynamical Behaviors ◽  
Complex Phenomena ◽  
And Control

<abstract><p>In this paper, we firstly formulate a new hyperchaotic Hamiltonian system and demonstrate the existence of multi-equilibrium points in the system. The characteristics of equilibrium points, Lyapunov exponents and Poincaré sections are studied. Secondly, we investigate the complex dynamical behaviors of the system under holonomic constraint and nonholonomic constraint, respectively. The results show that the hyperchaotic system can generated by introducing constraint. Additionally, the hyperchaos control of the system is achieved by applying linear feedback control. The numerical simulations are carried out in order to analyze the complex phenomena of the systems.</p></abstract>

A New 7D Hyperchaotic System with Five Positive Lyapunov Exponents Coined

2018 ◽  
Vol 28 (05) ◽  
pp. 1850057 ◽  
Author(s):  
Qigui Yang ◽  
Daoyu Zhu ◽  
Lingbing Yang
Keyword(s):  
Lyapunov Exponents ◽  
Lorenz System ◽  
Linear Feedback ◽  
Hyperchaotic System ◽  
Nonlinear Feedback ◽  
Feedback Controllers ◽  
Dynamical Behaviors ◽  
The Lorenz System ◽  
Hyperbolic Equilibrium ◽  
Good Agreement

This paper reports the finding of a new seven-dimensional (7D) autonomous hyperchaotic system, which is obtained by coupling a 1D linear system and a 6D hyperchaotic system that is constructed by adding two linear feedback controllers and a nonlinear feedback controller to the Lorenz system. This hyperchaotic system has very simple algebraic structure but can exhibit complex dynamical behaviors. Of particular interest is that it has a hyperchaotic attractor with five positive Lyapunov exponents and a unique equilibrium in a large range of parameters. Numerical analysis of phase trajectories, Lyapunov exponents, bifurcation, power spectrum and Poincaré projections verifies the existence of hyperchaotic and chaotic attractors. Moreover, stability of the hyperbolic equilibrium is analyzed and a complete mathematical characterization for 7D Hopf bifurcation is given. Finally, circuit experiment implements the hyperchaotic attractor of the 7D system, showing very good agreement with the simulation results.

A HYPERCHAOTIC SYSTEM WITH A FOUR-WING ATTRACTOR

2009 ◽  
Vol 20 (02) ◽  
pp. 323-335 ◽  
Author(s):  
GUOSI HU ◽  
BO YU
Keyword(s):  
System Dynamics ◽  
Lyapunov Exponents ◽  
Computer Simulations ◽  
Chaotic System ◽  
Bifurcation Analysis ◽  
Topological Structure ◽  
Hyperchaotic System ◽  
Wide Range ◽  
New Chaotic System

Recently, there are many methods for constructing multi-wing/multi-scroll or hyperchaotic attractors; however, it has been noticed that the attractors with both multi-wing topological structure and hyperchaotic characteristic rarely exist. A new chaotic system, obtained by making the change on coordinate to the Hu chaotic system, can generate very complex attractors with four-wing topological structure and three positive Lyapunov exponents over a wide range of parameters. The influence of parameters varying to system dynamics is analyzed, computer simulations and bifurcation analysis is also verified in this paper.

scholarly journals Distributed dynamic simulations of networked control and building performance applications

SIMULATION ◽  
2017 ◽  
Vol 94 (2) ◽  
pp. 145-161
Author(s):  
Azzedine Yahiaoui
Keyword(s):  
Control Systems ◽  
Dynamic Simulation ◽  
Minimum Energy ◽  
Building Performance ◽  
Simulation Environment ◽  
Dynamic Simulations ◽  
Wide Range ◽  
Automation And Control ◽  
And Control ◽  
Building Performance Applications

The use of computer-based automation and control systems for smart sustainable buildings, often so-called Automated Buildings (ABs), has become an effective way to automatically control, optimize, and supervise a wide range of building performance applications over a network while achieving the minimum energy consumption possible, and in doing so generally refers to Building Automation and Control Systems (BACS) architecture. Instead of costly and time-consuming experiments, this paper focuses on using distributed dynamic simulations to analyze the real-time performance of network-based building control systems in ABs and improve the functions of the BACS technology. The paper also presents the development and design of a distributed dynamic simulation environment with the capability of representing the BACS architecture in simulation by run-time coupling two or more different software tools over a network. The application and capability of this new dynamic simulation environment are demonstrated by an experimental design in this paper.

A Novel Hyperchaotic System With Adaptive Control, Synchronization, and Circuit Simulation

2018 ◽  
pp. 382-419 ◽  
Author(s):  
Sundarapandian Vaidyanathan ◽  
Ahmad Taher Azar ◽  
Aceng Sambas ◽  
Shikha Singh ◽  
Kammogne Soup Tewa Alain ◽  
...  
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Dissipative System ◽  
Phase Portraits ◽  
Hyperchaotic System ◽  
Qualitative Properties ◽  
New Hyperchaotic System

This chapter announces a new four-dimensional hyperchaotic system having two positive Lyapunov exponents, a zero Lyapunov exponent, and a negative Lyapunov exponent. Since the sum of the Lyapunov exponents of the new hyperchaotic system is shown to be negative, it is a dissipative system. The phase portraits of the new hyperchaotic system are displayed with both two-dimensional and three-dimensional phase portraits. Next, the qualitative properties of the new hyperchaotic system are dealt with in detail. It is shown that the new hyperchaotic system has three unstable equilibrium points. Explicitly, it is shown that the equilibrium at the origin is a saddle-point, while the other two equilibrium points are saddle-focus equilibrium points. Thus, it is shown that all three equilibrium points of the new hyperchaotic system are unstable. Numerical simulations with MATLAB have been shown to validate and demonstrate all the new results derived in this chapter. Finally, a circuit design of the new hyperchaotic system is implemented in MultiSim to validate the theoretical model.

A New 6D Hyperchaotic System with Four Positive Lyapunov Exponents Coined

2015 ◽  
Vol 25 (04) ◽  
pp. 1550060 ◽  
Author(s):  
Qigui Yang ◽  
Waleed Mahgoub Osman ◽  
Chuntao Chen
Keyword(s):  
Lyapunov Exponents ◽  
Lorenz System ◽  
Feedback Controller ◽  
Linear Feedback ◽  
Hyperchaotic System ◽  
Nonlinear Feedback ◽  
Dynamical Behaviors ◽  
Linear Feedback Controller ◽  
The Lorenz System ◽  
Hyperbolic Equilibrium

This paper reports the finding of a new six-dimensional (6D) autonomous hyperchaotic system, which is obtained by coupling a 1D linear system and a 5D hyperchaotic system that is constructed by adding a linear feedback controller and a nonlinear feedback controller to the Lorenz system. This hyperchaotic system has very simple algebraic structure but can exhibit complex dynamical behaviors. Of particular interest is that it has a hyperchaotic attractor with four positive Lyapunov exponents and a unique equilibrium in a large range of parameters. Numerical analysis of phase trajectories, Lyapunov exponents, bifurcation, power spectrum and Poincaré projections verifies the existence of the hyperchaotic and chaotic attractors. In addition, stability of the hyperbolic equilibrium is analyzed and two complete mathematical characterizations for 6D Hopf bifurcation are given.

scholarly journals Dynamics Analysis and Control of a Five-Term Fractional-Order System

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Li-xin Yang ◽  
Xiao-jun Liu
Keyword(s):  
Fractional Order ◽  
Equilibrium Points ◽  
Fractional Order System ◽  
Phase Portraits ◽  
Order System ◽  
Bifurcation Diagrams ◽  
Compound Structure ◽  
Dynamical Properties ◽  
The Stability ◽  
And Control

This paper proposes a new fractional-order chaotic system with five terms. Firstly, basic dynamical properties of the fractional-order system are investigated in terms of the stability of equilibrium points, Jacobian matrices theoretically. Furthermore, rich dynamics with interesting characteristics are demonstrated by phase portraits, bifurcation diagrams numerically. Besides, the control problem of the new fractional-order system is discussed via numerical simulations. Our results demonstrate that the new fractional-order system has compound structure.

Control of a Fractional-Order Arneodo System

2011 ◽  
Vol 383-390 ◽  
pp. 4405-4412 ◽  
Author(s):  
Kun Zhang ◽  
Hua Wang ◽  
Hui Tao Wang
Keyword(s):  
Stability Analysis ◽  
Theoretical Analysis ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Numerical Results ◽  
Linear Feedback ◽  
Order System ◽  
Feedback Controllers ◽  
Specific Choice ◽  
Work Stability

In this work, stability analysis of the Fractional-Order Arneodo system is studied by using the fractional Routh-Hurwitz criteria. Furthermore, the fractional Routh-Hurwitz conditions are used to control chaos in the proposed fractional-order system to its equilibria. Based on the fractional Routh-Hurwitz conditions and using specific choice of linear feedback controllers, it is shown that the Arneodo system is controlled to its equilibrium points. Numerical results show the effectiveness of the theoretical analysis.

Construction of Higher-Dimensional Hyperchaotic Systems with a Maximum Number of Positive Lyapunov Exponents under Average Eigenvalue Criteria

2019 ◽  
Vol 28 (09) ◽  
pp. 1950151
Author(s):  
Jianbin He ◽  
Simin Yu
Keyword(s):  
Lyapunov Exponents ◽  
Equilibrium Points ◽  
Control Period ◽  
Threshold Value ◽  
Hyperchaotic System ◽  
Positive Real ◽  
Controlled System ◽  
Number Formula ◽  
And Performance ◽  
Hyperchaotic Systems

Over the last 40 years, the design of [Formula: see text]-dimensional hyperchaotic systems with a maximum number ([Formula: see text]) of positive Lyapunov exponents has been an open problem for research. Nowadays it is not difficult to design [Formula: see text]-dimensional hyperchaotic systems with less than ([Formula: see text]) positive Lyapunov exponents, but it is still extremely difficult to design an [Formula: see text]-dimensional hyperchaotic system with the maximum number ([Formula: see text]) of positive Lyapunov exponents. This paper aims to resolve this challenging problem by developing a chaotification approach using average eigenvalue criteria. The approach consists of four steps: (i) a globally bounded controlled system is designed based on an asymptotically stable nominal system with a uniformly bounded controller; (ii) a closed-loop pole assignment technique is utilized to ensure that the numbers of eigenvalues with positive real parts of the controlled system be equal to ([Formula: see text]) and ([Formula: see text]), respectively, at two saddle-focus equilibrium points; (iii) the number of average eigenvalues with positive real parts is ensured to be equal to ([Formula: see text]) for the controlled system over a given control period; (iv) the smallest value of the positive real parts of the average eigenvalues is ensured to be greater than a given threshold value. Finally, the paper is closed with some typical examples which illustrate the feasibility and performance of the proposed design methodology.

scholarly journals Chaotic behavior analysis and control of a toxin producing phytoplankton and zooplankton system based on linear feedback

Filomat ◽  
2018 ◽  
Vol 32 (11) ◽  
pp. 3779-3789 ◽  
Author(s):  
Yadong Liu ◽  
Wenjun Liu
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Linear Feedback ◽  
Linear Feedback Control ◽  
The Stability ◽  
And Control ◽  
Fractional Orders

In this paper, we study the dynamic behavior and control of the fractional-order nutrientphytoplankton-zooplankton system. First, we analyze the stability of the fractional-order nutrient-plankton system and get the critical stable value of fractional orders. Then, by applying the linear feedback control and Routh-Hurwitz criterion, we yield the sufficient conditions to stabilize the system to its equilibrium points. Finally, Under a modified fractional-order Adams-Bashforth-Monlton algorithm, we simulate the results respectively.

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