Dynamics and Synchronization of a Novel Hyperchaotic System Without Equilibrium

A novel four-dimensional continuous-time autonomous hyperchaotic system which has no equilibrium is proposed in this paper. By starting from a third-order chaotic system and introducing a further variable performing state feedback, a four-dimensional system exhibiting hyperchaos is obtained. The basic dynamical properties of this system are investigated, such as equilibria and stability, Lyapunov exponent spectrum, and bifurcation diagrams. Furthermore, synchronization via diffusive coupling or control has been addressed. In the latter, parameter identification and synchronization are performed simultaneously. The circuit realization and experimental results are also presented.

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A Switched Hyperchaotic System and Analysis of Dynamical Properties

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.452-453.511 ◽

2012 ◽

Vol 452-453 ◽

pp. 511-515

Author(s):

Bian Li ◽

Ai Xue Qi ◽

Wei Bing Li

Keyword(s):

Lyapunov Exponent ◽

Numerical Simulations ◽

Bifurcation Diagram ◽

Experimental Results ◽

Hyperchaotic System ◽

Symbolic Function ◽

Dynamical Properties ◽

Lyapunov Exponent Spectrum

This paper introduces a new switched hyperchaotic system by utilizing symbolic function. The switched hyperchaotic system converts its states from one subsystem to another via symbolic functions. By the analysis of its dynamics, symmetry, dissipativity, Lyapunov exponent spectrum and bifurcation diagram of the system. The system is implemented by the FPGA hardware. It is shown that the experimental results are identical with numerical simulations, and the chaotic trajectories are much more complex.

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Design of 9-D global chaotic system and its application in secure communication

Circuit World ◽

10.1108/cw-03-2020-0042 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Meiting Liu ◽

Wenxin Yu ◽

Junnian Wang ◽

Yu Chen ◽

Yuyan Bian

Keyword(s):

Chaotic System ◽

Secure Communication ◽

Dimensional System ◽

Hyperchaotic System ◽

Secret Key ◽

Complex Dynamic ◽

Content Type ◽

Key Space ◽

C0 Complexity ◽

Lyapunov Exponent Spectrum

Purpose In this paper, a nine-dimensional chaotic system is designed and applied to secure communication. Design/methodology/approach Firstly, the equilibrium characteristics, dissipativity, bifurcation diagram and Lyapunov exponent spectrum are used to analyze the relevant characteristics of the proposed nine-dimensional chaotic system. In the analysis of Lyapunov exponential spectrum, when changing the linear parameters, the system shows two states, hyperchaos and chaos. For secure communication, there is a large secret key space. Secondly, C0 complexity and SEcomplexity of the system are analyzed, which shows that the system has sequences closer to random sequences. Findings The proposed nine-dimensional system has a large key space and more complex dynamic characteristics Originality/value The results show that the proposed nine-dimensional hyperchaotic system has excellent encryption capabilities and can play an important role in the field of secure communication.

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Dynamical properties of a kind of SIR model with constant vaccination rate and impulsive state feedback control

International Journal of Biomathematics ◽

10.1142/s1793524517500930 ◽

2017 ◽

Vol 10 (07) ◽

pp. 1750093 ◽

Cited By ~ 8

Author(s):

Hongjian Guo ◽

Lansun Chen ◽

Xinyu Song

Keyword(s):

Periodic Solution ◽

Feedback Control ◽

State Feedback ◽

Sir Model ◽

Vaccination Rate ◽

State Feedback Control ◽

Dimensional System ◽

Impulsive State Feedback Control ◽

Dynamical Properties ◽

The Government

Considering the fact that the production and provision of some vaccines are ordered and governed by the government according to the history data of disease, a kind of SIR model with constant vaccination rate and impulsive state feedback control is presented. The dynamical properties of semi-continuous three-dimensional SIR system can be obtained by discussing the properties of the corresponding two-dimensional system in the limit set. The existence and uniqueness of order-1 periodic solution are discussed by using the successive function and the compression mapping theorem. A new theorem for the orbital stability of order-1 periodic solution is proved by geometric method. Finally, numerical simulations are given to verify the mathematical results and some conclusions are given. The results show that the disease can be controlled to a lower level by means of impulsive state feedback control strategy, but cannot be eradicated.

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A NEW HYPERCHAOTIC SYSTEM AND ITS CIRCUIT IMPLEMENTATION

International Journal of Bifurcation and Chaos ◽

10.1142/s021812741002640x ◽

2010 ◽

Vol 20 (04) ◽

pp. 1201-1208 ◽

Cited By ~ 9

Author(s):

MINGHUA LIU ◽

JIUCHAO FENG ◽

CHI K. TSE

Keyword(s):

Nonlinear Control ◽

Bifurcation Diagram ◽

Continuous Time ◽

Control Parameter ◽

Electronic Circuit ◽

Three Dimensional ◽

Hyperchaotic System ◽

Circuit Implementation ◽

Time Autonomous ◽

New Hyperchaotic System

A four-dimensional continuous-time autonomous hyperchaotic system is proposed in this letter. This system is constructed by incorporating a nonlinear control to a three-dimensional continuous-time autonomous chaotic system. The hyperchaotic system is analyzed by studying the spectrum of Lyapunov exponents and the corresponding bifurcation diagram. The system exhibits chaotic, periodic, hyperchaotic behaviors for different values of a selected control parameter. Also, a simple electronic circuit is designed and implemented. Simulations and experimental observations verify the analytical results.

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

Complexity ◽

10.1155/2020/7106861 ◽

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.

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