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.

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.

Applicable Image Security Based on New Hyperchaotic System

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2290
Author(s):  
Jingya Wang ◽  
Xianhua Song ◽  
Huiqiang Wang ◽  
Ahmed A. Abd El-Latif
Keyword(s):  
Image Encryption ◽  
Complexity Analysis ◽  
Dynamical Behavior ◽  
Logistic Map ◽  
Hyperchaotic System ◽  
Two Dimensional ◽  
Analysis Methods ◽  
Lyapunov Index ◽  
And Diffusion ◽  
New Hyperchaotic System

Hyperchaotic systems are widely applied in the cryptography domain on account of their more complex dynamical behavior. In view of this, the greatest contribution of this paper is that a two-dimensional Sine coupling Logistic modulated Sine (2D-SCLMS) system is proposed based on Logistic map and Sine map. By a series of analyses, including Lyapunov index (LE), 0–1 test, two complexity analysis methods, and two entropy analysis methods, it is concluded that the new 2D-SCLMS map is hyperchaotic with a wider range of chaos and more complex randomness. The new system combined with two-dimensional Logistic-Sine Coupling Mapping (2D-LSCM) is further applied to an image encryption application. SHA-384 is used to generate the initial values and parameters of the two chaotic systems. Symmetric keys are generated during this operation, which can be applied to the proposed image encryption and decryption algorithms. The encryption process and the decryption process of the new image encryption approaches mainly include pixel scrambling, exclusive NOR (Xnor), and diffusion operations. Multiple experiments illustrate that this scheme has higher security and lower time complexity.

scholarly journals A Multistable Chaotic Jerk System with Coexisting and Hidden Attractors: Dynamical and Complexity Analysis, FPGA-Based Realization, and Chaos Stabilization Using a Robust Controller

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 569 ◽  
Author(s):  
Heng Chen ◽  
Shaobo He ◽  
Ana Dalia Pano Azucena ◽  
Amin Yousefpour ◽  
Hadi Jahanshahi ◽  
...  
Keyword(s):  
Complexity Analysis ◽  
Sliding Mode ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Constant Term ◽  
Successful Implementation ◽  
Hidden Attractors ◽  
Field Programmable ◽  
Jerk System

In the present work, a new nonequilibrium four-dimensional chaotic jerk system is presented. The proposed system includes only one constant term and has coexisting and hidden attractors. Firstly, the dynamical behavior of the system is investigated using bifurcation diagrams and Lyapunov exponents. It is illustrated that this system either possesses symmetric equilibrium points or does not possess an equilibrium. Rich dynamics are found by varying system parameters. It is shown that the system enters chaos through experiencing a cascade of period doublings, and the existence of chaos is verified. Then, coexisting and hidden chaotic attractors are observed, and basin attraction is plotted. Moreover, using the multiscale C0 algorithm, the complexity of the system is investigated, and a broad area of high complexity is displayed in the parameter planes. In addition, the chaotic behavior of the system is studied by field-programmable gate array implementation. A novel methodology to discretize, simulate, and implement the proposed system is presented, and the successful implementation of the proposed system on FPGA is verified through the simulation outcome. Finally, a robust sliding mode controller is designed to suppress the chaotic behavior of the system. To deal with unexpected disturbances and uncertainties, a disturbance observer is developed along with the designed controller. To show the successful performance of the designed control scheme, numerical simulations are also presented.

EXPERIMENTAL VERIFICATION OF A FOUR-DIMENSIONAL CHUA'S SYSTEM AND ITS FRACTIONAL ORDER CHAOTIC ATTRACTORS

2009 ◽  
Vol 19 (08) ◽  
pp. 2473-2486 ◽  
Author(s):  
LING LIU ◽  
CHONGXIN LIU ◽  
YANBIN ZHANG
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Analog Circuit ◽  
Equilibrium Points ◽  
Phase Portraits ◽  
Chaotic Oscillator ◽  
Oscillation Circuit ◽  
Mapping Parameter ◽  
Time Autonomous ◽  
First Time

This paper introduces a modified Chua's system which is a smooth four-dimensional continuous-time autonomous chaotic system with a cubic nonlinearity. Some dynamical behaviors of this 4-D Chua's system are further investigated by means of Poincaré mapping, parameter phase portraits, equilibrium points, bifurcations and calculated Lyapunov exponents. Moreover, using RC-opamp and analog multiplier we describe a simple electronic circuit for hardware implementation of the 4-D Chua's system which differ from previously reported Chua's circuits. Various attractors of experimental results from this chaotic oscillator are in good agreement with theoretical analysis. In particular, based on the approximation theory of fractional-order operator, a relevant analog circuit diagram of this fractional-order modified Chua's system is designed with α = 0.9. Observation results demonstrate that chaos exists indeed in this fractional-order modified Chua's system with an order as low as 3.6. This fractional-order oscillation circuit, for the first time in the literature, realizes high-dimensional Chua's chaotic system.

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 Chaotic Dynamics of an Airfoil with Higher-Order Plunge and Pitch Stiffnesses in Incompressible Flow

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Karthikeyan Rajagopal ◽  
Yesgat Admassu ◽  
Riessom Weldegiorgis ◽  
Prakash Duraisamy ◽  
Anitha Karthikeyan
Keyword(s):  
Chaotic Dynamics ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
State Space Model ◽  
Higher Order ◽  
Countable Number ◽  
State Equations ◽  
Proposed Model ◽  
Dynamical Properties ◽  
First Time

Dynamical properties of a two-dimensional airfoil model with higher-order strong nonlinearities are investigated. Firstly, a state-space model is derived considering the plunge and pitch stiffnesses as generalized functions. Then, a stiffness function having square, cubic, and fifth-power nonlinearities is considered for both plunging and pitching stiffnesses, and the dimensionless state equations are derived. Various dynamical properties of the proposed model are investigated using equilibrium points, eigenvalues, and Lyapunov exponents. To further analyze the dynamical behavior of the system, bifurcation plots are derived. It is interesting to note that the new airfoil model with higher-order nonlinearities shows multistability with changing airspeed, and there are infinitely countable number of coexisting attractors generally called as megastability. Both multistability and megastability features of the airfoil model were not captured earlier in the literatures. To be clear, it is the first time a megastable feature is exposed in a physical system. Finally, to analyze the multifrequency effects of the airfoil model, we have presented the bicoherence plots.

scholarly journals Dynamic Analysis and Circuit Realization of a Novel No-Equilibrium 5D Memristive Hyperchaotic System with Hidden Extreme Multistability

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Qiuzhen Wan ◽  
Zhaoteng Zhou ◽  
Wenkui Ji ◽  
Chunhua Wang ◽  
Fei Yu
Keyword(s):  
Initial Conditions ◽  
Hyperchaotic System ◽  
Circuit Realization ◽  
System Parameters ◽  
Dynamical Characteristics ◽  
Offset Boosting ◽  
Extreme Multistability ◽  
Hidden Extreme Multistability ◽  
Dynamic Attractors ◽  
Lyapunov Exponent Spectrum

In this paper, a novel no-equilibrium 5D memristive hyperchaotic system is proposed, which is achieved by introducing an ideal flux-controlled memristor model and two constant terms into an improved 4D self-excited hyperchaotic system. The system parameters-dependent and memristor initial conditions-dependent dynamical characteristics of the proposed memristive hyperchaotic system are investigated in terms of phase portrait, Lyapunov exponent spectrum, bifurcation diagram, Poincaré map, and time series. Then, the hidden dynamic attractors such as periodic, quasiperiodic, chaotic, and hyperchaotic attractors are found under the variation of its system parameters. Meanwhile, the most striking phenomena of hidden extreme multistability, transient hyperchaotic behavior, and offset boosting control are revealed for appropriate sets of the memristor and other initial conditions. Finally, a hardware electronic circuit is designed, and the experimental results are well consistent with the numerical simulations, which demonstrate the feasibility of this novel 5D memristive hyperchaotic system.

Genetic Diversity of Basil (Ocimum spp. - Lamiaceae) Based on RAPD Markers and Volatile Oil Constituents

HortScience ◽  
1998 ◽  
Vol 33 (3) ◽  
pp. 492f-493
Author(s):  
Roberto F. Vieira ◽  
James E. Simon ◽  
Peter Goldsbrough ◽  
Antonio Figueira
Keyword(s):  
Genetic Diversity ◽  
Molecular Markers ◽  
Rapd Markers ◽  
Volatile Oil ◽  
Essential Oil Composition ◽  
Oil Composition ◽  
Traditional Medicines ◽  
The Tropics ◽  
High Degree ◽  
First Time

Essential oils extracted from basil (Ocimum spp.) by steam distillation are used to flavor foods, oral products, in fragrances, and in traditional medicines. The genus Ocimum contains around 30 species native to the tropics and subtropics, with some species naturalized and/or cultivated in temperate areas. Interand intraspecific hybridization have created significant confusion in the botanical systematics of this genus. Taxonomy of basil (O. basilicum) is also complicated by the existence of numerous varieties, cultivars, and chemotypes within the species that do not differ significantly in morphology. In this study we are using RAPD markers and volatile oil composition to characterize the genetic diversity among the most economically important Ocimum species. We hypothesize that the genetic similarity revealed by molecular markers will more accurately reflect the morphological and chemical differences in Ocimum than essential oil composition per se. Preliminary research using five Ocimum species, four undetermined species, and eight varieties of O. basilicum (a total of 19 accessions) generated 107 polymorphic fragments amplified with 19 primers. RAPDs are able to discriminate between Ocimum species, but show a high degree of similarity between O. basilicum varieties. The genetic distance between nine species and among 55 accessions within the species O. americanum, O. basilicum, O. campechianum, O. × citriodorum, O. gratissimum, O. kilimandscharium, O. minimum, O. selloi, and O. tenuiflorum will be analyzed by matrix of similarity and compared to the volatile oil profile. This research will for the first time apply molecular markers to characterize the genetic diversity of Ocimum associate with volatile oil constituent.

Characterization of SrBi2Nb2O9 Thin Films Prepared by Sol Gel Technique

1996 ◽  
Vol 459 ◽  
Author(s):  
E. Ching-Prado ◽  
W. Pérez ◽  
A. Reynés-Figueroa ◽  
R. S. Katiyar ◽  
D. Ravichandran ◽  
...  
Keyword(s):  
Thin Films ◽  
Raman Band ◽  
Sol Gel ◽  
Orthorhombic Symmetry ◽  
X Ray Diffraction ◽  
Ft Ir ◽  
Gel Technique ◽  
High Degree ◽  
First Time

ABSTRACTThin films of SrBi2Nb2O9 (SBN) with thicknesses of 0.1, 0.2, and 0.4 μ were grown by Sol-gel technique on silicon, and annealed at 650°C. The SBN films were investigated by Raman scatering for the first time. Raman spectra in some of the samples present bands around 60, 167, 196, 222, 302, 451, 560, 771, 837, and 863 cm−1, which correspond to the SBN formation. The study indicates that the films are inhomogeneous, and only in samples with thicknesses 0.4 μ the SBN material was found in some places. The prominent Raman band around 870 cm−1, which is the A1g mode of the orthorhombic symmetry, is assigned to the symmetric stretching of the NbO6 octahedrals. The frequency of this band is found to shift in different places in the same sample, as well as from sample to sample. The frequency shifts and the width of the Raman bands are discussed in term of ions in non-equilibrium positions. FT-IR spectra reveal a sharp peak at 1260 cm−1, and two broad bands around 995 and 772 cm−1. The bandwidths of the latter two bands are believed to be associated with the presence of a high degree of defects in the films. The experimental results of the SBN films are compared with those obtained in SBT (T=Ta) films. X-ray diffraction and SEM techniques are also used for the structural characterization.

Optimal Synchronization of a Memristive Chaotic Circuit

2016 ◽  
Vol 26 (06) ◽  
pp. 1650093 ◽  
Author(s):  
Michaux Kountchou ◽  
Patrick Louodop ◽  
Samuel Bowong ◽  
Hilaire Fotsin ◽  
Jurgen Kurths
Keyword(s):  
Numerical Simulations ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Analog Circuit ◽  
Electronic Circuit ◽  
Dynamical Behavior ◽  
Circuit Implementation ◽  
Chaotic Circuit ◽  
Dynamical Properties ◽  
Analog Circuit Implementation

This paper deals with the problem of optimal synchronization of two identical memristive chaotic systems. We first study some basic dynamical properties and behaviors of a memristor oscillator with a simple topology. An electronic circuit (analog simulator) is proposed to investigate the dynamical behavior of the system. An optimal synchronization strategy based on the controllability functions method with a mixed cost functional is investigated. A finite horizon is explicitly computed such that the chaos synchronization is achieved at an established time. Numerical simulations are presented to verify the effectiveness of the proposed synchronization strategy. Pspice analog circuit implementation of the complete master-slave-controller systems is also presented to show the feasibility of the proposed scheme.

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