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>

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 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.

scholarly journals MATHEMATICAL MODEL OF THREE SPECIES FOOD CHAIN INTERACTION WITH MIXED FUNCTIONAL RESPONSE

2012 ◽  
Vol 09 ◽  
pp. 334-340 ◽  
Author(s):  
MADA SANJAYA WS ◽  
ISMAIL BIN MOHD ◽  
MUSTAFA MAMAT ◽  
ZABIDIN SALLEH
Keyword(s):  
Mathematical Model ◽  
Functional Response ◽  
Food Chain ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Bifurcation Points ◽  
Dynamical Behaviors ◽  
Practical Life ◽  
Parameter Values ◽  
Chain Interaction

In this paper, we study mathematical model of ecology with a tritrophic food chain composed of a classical Lotka-Volterra functional response for prey and predator, and a Holling type-III functional response for predator and super predator. There are two equilibrium points of the system. In the parameter space, there are passages from instability to stability, which are called Hopf bifurcation points. For the first equilibrium point, it is possible to find bifurcation points analytically and to prove that the system has periodic solutions around these points. Furthermore the dynamical behaviors of this model are investigated. Models for biologically reasonable parameter values, exhibits stable, unstable periodic and limit cycles. The dynamical behavior is found to be very sensitive to parameter values as well as the parameters of the practical life. Computer simulations are carried out to explain the analytical findings.

Dynamical Analysis and Circuit Simulation of a New Fractional-Order Hyperchaotic System and Its Discretization

2016 ◽  
Vol 26 (13) ◽  
pp. 1650222 ◽  
Author(s):  
A. M. A. El-Sayed ◽  
A. Elsonbaty ◽  
A. A. Elsadany ◽  
A. E. Matouk
Keyword(s):  
Fractional Order ◽  
Initial Conditions ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Control Technique ◽  
Order System ◽  
Qualitative Behavior ◽  
Hyperchaotic System

This paper presents an analytical framework to investigate the dynamical behavior of a new fractional-order hyperchaotic circuit system. A sufficient condition for existence, uniqueness and continuous dependence on initial conditions of the solution of the proposed system is derived. The local stability of all the system’s equilibrium points are discussed using fractional Routh–Hurwitz test. Then the analytical conditions for the existence of a pitchfork bifurcation in this system with fractional-order parameter less than 1/3 are provided. Conditions for the existence of Hopf bifurcation in this system are also investigated. The dynamics of discretized form of our fractional-order hyperchaotic system are explored. Chaos control is also achieved in discretized system using delay feedback control technique. The numerical simulation are presented to confirm our theoretical analysis via phase portraits, bifurcation diagrams and Lyapunov exponents. A text encryption algorithm is presented based on the proposed fractional-order system. The results show that the new system exhibits a rich variety of dynamical behaviors such as limit cycles, chaos and transient phenomena where fractional-order derivative represents a key parameter in determining system qualitative behavior.

scholarly journals Dynamical Analysis, Synchronization, Circuit Design, and Secure Communication of a Novel Hyperchaotic System

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-23 ◽  
Author(s):  
Li Xiong ◽  
Zhenlai Liu ◽  
Xinguo Zhang
Keyword(s):  
Secure Communication ◽  
Control Method ◽  
Dynamical Behavior ◽  
Control Level ◽  
Lyapunov Stability Theory ◽  
Dynamical Analysis ◽  
Linear Feedback ◽  
Hyperchaotic System ◽  
Error System ◽  
New Hyperchaotic System

This paper is devoted to introduce a novel fourth-order hyperchaotic system. The hyperchaotic system is constructed by adding a linear feedback control level based on a modified Lorenz-like chaotic circuit with reduced number of amplifiers. The local dynamical entities, such as the basic dynamical behavior, the divergence, the eigenvalue, and the Lyapunov exponents of the new hyperchaotic system, are all investigated analytically and numerically. Then, an active control method is derived to achieve global chaotic synchronization of the novel hyperchaotic system through making the synchronization error system asymptotically stable at the origin based on Lyapunov stability theory. Next, the proposed novel hyperchaotic system is applied to construct another new hyperchaotic system with circuit deformation and design a new hyperchaotic secure communication circuit. Furthermore, the implementation of two novel electronic circuits of the proposed hyperchaotic systems is presented, examined, and realized using physical components. A good qualitative agreement is shown between the simulations and the experimental results around 500 kHz and below 1 MHz.

scholarly journals Theoretical Analysis and Circuit Verification for Fractional-Order Chaotic Behavior in a New Hyperchaotic System

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Ling Liu ◽  
Chongxin Liu
Keyword(s):  
Fractional Order ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Circuit Diagram ◽  
Phase Portraits ◽  
Hyperchaotic System ◽  
Dynamical Behaviors ◽  
Mapping Parameter ◽  
New Hyperchaotic System ◽  
Observation Results

A novel nonlinear four-dimensional hyperchaotic system and its fractional-order form are presented. Some dynamical behaviors of this system are further investigated, including Poincaré mapping, parameter phase portraits, equilibrium points, bifurcations, and calculated Lyapunov exponents. A simple fourth-channel block circuit diagram is designed for generating strange attractors of this dynamical system. Specifically, a novel network module fractance is introduced to achieve fractional-order circuit diagram for hardware implementation of the fractional attractors of this nonlinear hyperchaotic system with order as low as 0.9. Observation results have been observed by using oscilloscope which demonstrate that the fractional-order nonlinear hyperchaotic attractors exist indeed in this new system.

scholarly journals A Novel Four-Dimensional Energy-Saving and Emission-Reduction System and Its Linear Feedback Control

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Minggang Wang ◽  
Hua Xu
Keyword(s):  
Feedback Control ◽  
Energy Saving ◽  
Emission Reduction ◽  
Carbon Emission ◽  
Equilibrium Points ◽  
Energy Development ◽  
Linear Feedback ◽  
Control Methods ◽  
Linear Feedback Control ◽  
New Energy

This paper reports a new four-dimensional energy-saving and emission-reduction chaotic system. The system is obtained in accordance with the complicated relationship between energy saving and emission reduction, carbon emission, economic growth, and new energy development. The dynamics behavior of the system will be analyzed by means of Lyapunov exponents and equilibrium points. Linear feedback control methods are used to suppress chaos to unstable equilibrium. Numerical simulations are presented to show these results.

A New Four-Dimensional Non-Hamiltonian Conservative Hyperchaotic System

2020 ◽  
Vol 30 (16) ◽  
pp. 2050242
Author(s):  
Shuangquan Gu ◽  
Baoxiang Du ◽  
Yujie Wan
Keyword(s):  
Analog Circuit ◽  
Complexity Analysis ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Hyperchaotic System ◽  
Attraction Basin ◽  
Hidden Extreme Multistability ◽  
High Degree ◽  
First Time ◽  
Lyapunov Exponent Spectrum

This paper presents a new four-dimensional non-Hamiltonian conservative hyperchaotic system. In the absence of equilibrium points in the system, the phase trajectories generated by the system have hidden features. The conservative features that vary with the parameter have been analyzed in detail by Lyapunov exponent spectrum, bifurcation diagram, the sum of Lyapunov exponents, and the fractional dimensions, and during the analysis, multiple quasi-periodic four-dimensional tori as well as hyperchaotic attractors have been observed. The Poincaré sections confirm these dynamic behaviors. Amidst the process of studying the dynamical behavior of the system with initial values, the hidden extreme multistability, and the initial offset boosting behavior, the results have been witnessed for the very first time in a conservative chaotic system. The phase diagram and attraction basin also confirm this assertion, while two complex transient transition behaviors have been observed. Moreover, through the introduction of a spectral entropy algorithm, the complexity analysis of the time sequences generated by the system have been performed and compared with the existing literature. The results show that the system has a high degree of complexity. The design and construction of the analog circuit of the system for simulation, the circuit experimental results are consistent with the numerical simulation, further verifying the physical realizability of the newly proposed system. This lays a good foundation for its practical application in engineering.

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.

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