Dynamic Analysis and FPGA Implementation of a Kolmogorov-Like Hyperchaotic System

2021 ◽  
Vol 31 (04) ◽  
pp. 2150052
Author(s):  
Xiaodong Jiao ◽  
Enzeng Dong ◽  
Zenghui Wang
Keyword(s):  
Vector Field ◽  
Numerical Analysis ◽  
Dynamic Analysis ◽  
Dynamic Systems ◽  
Spherical Function ◽  
Chaotic Systems ◽  
Complex Dynamics ◽  
Hyperchaotic System ◽  
Nist Tests ◽  
Dissipative Dynamic

Chaotic systems have high potential for engineering applications due to their extremely complex dynamics. In the paper, a five-dimensional (5D) Kolmogorov-like hyperchaotic system is proposed. First, the hyperchaotic property is uncovered, and numerical analysis shows that the system displays the coexistence of different kinds of attractors. This system presents a generalized form of fluid and forced-dissipative dynamic systems. The vector field of the hyperchaotic system is decomposed to inertial, internal, dissipative and external torques, respectively, and the energies are analyzed in detail. Then, the bound of the 5D dissipative hyperchaos is estimated with a constructed spherical function. Finally, the system passes the NIST tests and an FPGA platform is used to realize the hyperchaotic system.

scholarly journals Dynamic Analysis and Circuit Design of a Novel Hyperchaotic System with Fractional-Order Terms

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Abir Lassoued ◽  
Olfa Boubaker
Keyword(s):  
Dynamic Analysis ◽  
Circuit Design ◽  
Fractional Order ◽  
Potential Application ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Hyperchaotic System ◽  
Software Simulation ◽  
Simulation Results ◽  
Hyperchaotic Systems

A novel hyperchaotic system with fractional-order (FO) terms is designed. Its highly complex dynamics are investigated in terms of equilibrium points, Lyapunov spectrum, and attractor forms. It will be shown that the proposed system exhibits larger Lyapunov exponents than related hyperchaotic systems. Finally, to enhance its potential application, a related circuit is designed by using the MultiSIM Software. Simulation results verify the effectiveness of the suggested circuit.

Dynamic Analysis of the Pipe Lifting Mechanism on the Deepwater Pipelaying Vessel

2011 ◽  
Vol 199-200 ◽  
pp. 251-256
Author(s):  
Kai An Yu ◽  
Ke Yu Chen
Keyword(s):  
Numerical Analysis ◽  
Dynamic Analysis ◽  
High Efficiency ◽  
Transport Systems ◽  
Kinematic Pair ◽  
Analysis Method ◽  
Numerical Analysis Method ◽  
Upper Limit ◽  
Lifting Capacity ◽  
Limit Position

Based on requirements of pipe transport systems on deepwater pipelaying vessel, a new pipe lifting mechanism was designed. It was composed of crank-rocker and rocker-slider mechanism with good lifting capacity and high efficiency. When the slider went to the upper limit position, the mechanism could approximatively dwell, meeting the requirement for transverse conveyor operation. According to the theory of dynamics, numerical analysis method was used to the dynamic analysis of the mechanism. The results showed the maximum counterforce was at the joint between the rocker and ground, and this calculation could be a guideline for the kinematic pair structure designing.

MUTUAL AND SELF-COMPOUNDING OF CHAOTIC SYSTEMS

1996 ◽  
Vol 06 (04) ◽  
pp. 759-767
Author(s):  
R. SINGH ◽  
P.S. MOHARIR ◽  
V.M. MARU
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Dynamic Systems ◽  
Mantle Convection ◽  
Chaotic Systems ◽  
Compound System ◽  
Two Systems

The notion of compounding a chaotic system was introduced earlier. It consisted of varying the parameters of the compoundee system in proportion to the variables of the compounder system, resulting in a compound system which has in general higher Lyapunov exponents. Here, the notion is extended to self-compounding of a system with a real-earth example, and mutual compounding of dynamic systems. In the former, the variables in a system perturb its parameters. In the latter, two systems affect the parameters of each other in proportion to their variables. Examples of systems in such compounding relationships are studied. The existence of self-compounding is indicated in the geodynamics of mantle convection. The effect of mutual compounding is studied in terms of Lyapunov exponent variations.

Hidden Hyperchaotic Attractors in a New 5D System Based on Chaotic System with Two Stable Node-Foci

2019 ◽  
Vol 29 (07) ◽  
pp. 1950092 ◽  
Author(s):  
Qigui Yang ◽  
Lingbing Yang ◽  
Bin Ou
Keyword(s):  
Chaotic System ◽  
Stable Equilibrium ◽  
Complex Dynamics ◽  
Dynamical Evolution ◽  
Stable Node ◽  
Hyperchaotic System ◽  
Hidden Attractors ◽  
Circuit Realization ◽  
Switching Algorithm ◽  
Linear Controllers

This paper reports some hidden hyperchaotic attractors and complex dynamics in a new five-dimensional (5D) system with only two nonlinear terms. The system is generated by adding two linear controllers to an unusual 3D autonomous quadratic chaotic system with two stable node-foci. In particular, the hyperchaotic system without equilibrium or with only one stable equilibrium can generate two kinds of hidden hyperchaotic attractors with three positive Lyapunov exponents. Numerical methods not only verify the existence of such attractors and hyperchaotic attractors, but also show the dynamical evolution of this system. The 5D system has self-excited attractors and two types of hidden attractors with the change of its parameter. The parameter switching algorithm is further utilized to numerically approximate the attractor. Specifically, the hidden hyperchaotic attractor can be approximated by switching between two self-excited chaotic attractors. Finally, the circuit realization results are consistent with the numerical results.

The Jacobi Stability of a Lorenz-Type Multistable Hyperchaotic System with a Curve of Equilibria

2019 ◽  
Vol 29 (05) ◽  
pp. 1950062 ◽  
Author(s):  
Yuming Chen ◽  
Zongbin Yin
Keyword(s):  
Differential Geometry ◽  
Vector Field ◽  
Periodic Orbit ◽  
Curvature Tensor ◽  
Hyperchaotic System ◽  
Geometry Method ◽  
Parameter Condition

In this paper, a 4D Lorenz-type multistable hyperchaotic system with a curve of equilibria is investigated by using differential geometry method, i.e. with KCC-theory. Due to the deviation curvature tensor and its eigenvalues, the curve of equilibria of this hyperchaotic system is proved analytically to be Jacobi unstable under a certain parameter condition, and a periodic orbit of this system is proved numerically to be also Jacobi unstable. Furthermore, the dynamics of contravariant vector field near the curve of equilibria and the periodic orbit are studied, respectively, and their results comply absolutely with the above analysis of Jacobi stability.

Analysis on Hopf Bifurcation and Complexity of one Kind Financial System

2011 ◽  
Vol 48-49 ◽  
pp. 813-816 ◽  
Author(s):  
Qi Zhang ◽  
Jun Hai Ma
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Hopf Bifurcation ◽  
Dynamic Analysis ◽  
Dynamic Systems ◽  
Financial System ◽  
The Relationship ◽  
At Home

From a mathematical model of one kind complicated financial system, we make a dynamic analysis on this kind of system on the basis of studies of scholars both at home and abroad. We find characteristics of various dynamic systems driven by different parameters, and study possible Hopf bifurcation as well as the relationship between Hopf bifurcation and the values of parameters. Besides, we make use of algorithm to analyze complexity of the system. The results of numerical simulation prove that the theory used in the thesis is correct. This study is regarded with good theoretical and practical value.

ACTIVE TRACKING CONTROL OF THE HYPERCHAOTIC LORENZ SYSTEM

2008 ◽  
Vol 22 (19) ◽  
pp. 1859-1865 ◽  
Author(s):  
XINGYUAN WANG ◽  
DAHAI NIU ◽  
MINGJUN WANG
Keyword(s):  
Numerical Simulation ◽  
Tracking Control ◽  
Chaotic Systems ◽  
Lorenz System ◽  
The Self ◽  
Hyperchaotic System ◽  
Reference Signals ◽  
Tracking Controller ◽  
Hyperchaotic Lorenz System ◽  
Simulation Results

A nonlinear active tracking controller for the four-dimensional hyperchaotic Lorenz system is designed in the paper. The controller enables this hyperchaotic system to track all kinds of reference signals, such as the sinusoidal signal. The self-synchronization of the hyperchaotic Lorenz system and the different-structure synchronization with other chaotic systems can also be realized. Numerical simulation results show the effectiveness of the controller.

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