A New Five-Dimensional Hyperchaotic System with Six Coexisting Attractors

This article introduces a new hyperchaotic system of four-dimensional autonomous ordinary differential equations, with only cubic cross-product nonlinearities, which can respectively display two hyperchaotic attractors with only nonhyperbolic equilibria line. Several issues such as basic dynamical behaviors, routes to chaos, bifurcations, periodic windows, and the compound structure of the new hyperchaotic and chaotic system are investigated, either theoretically or numerically. Of particular interest is the fact that the two coexisting attractors of the new hyperchaotic system are symmetrical, and this hyperchaotic system can generate plenty of complex dynamics including two coexisting chaotic or periodic attractors. Moreover, some chaotic features of the attractor are justified numerically. Finally, 0-1 test is used to analyze and describe the complex chaotic dynamic behavior of the new system.

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FPGA design and circuit implementation of a new four-dimensional multistable hyperchaotic system with coexisting attractors

International Journal of Computer Applications in Technology ◽

10.1504/ijcat.2020.10034168 ◽

2020 ◽

Vol 64 (3) ◽

pp. 223

Author(s):

Aceng Sambas ◽

Omar Guillén Fernández ◽

Leutcho Gervais Dolvis ◽

Sundarapandian Vaidyanathan ◽

Esteban Tlelo Cuautle

Keyword(s):

Hyperchaotic System ◽

Circuit Implementation ◽

Fpga Design ◽

Coexisting Attractors

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A No-Equilibrium Hyperchaotic System and Its Fractional-Order Form

Mathematical Problems in Engineering ◽

10.1155/2017/3927184 ◽

2017 ◽

Vol 2017 ◽

pp. 1-11 ◽

Cited By ~ 7

Author(s):

Duy Vo Hoang ◽

Sifeu Takougang Kingni ◽

Viet-Thanh Pham

Keyword(s):

Fractional Order ◽

Chaotic Behavior ◽

Chaotic Attractors ◽

Dimensional System ◽

Hyperchaotic System ◽

Equilibrium System ◽

Coexisting Attractors ◽

Amplitude Control ◽

Dynamical Behaviors ◽

Point Attractor

No-equilibrium system with chaotic behavior has attracted considerable attention recently because of its hidden attractor. We study a new four-dimensional system without equilibrium in this work. The new no-equilibrium system exhibits hyperchaos and coexisting attractors. Amplitude control feature of the system is also discovered. The commensurate fractional-order version of the proposed system is studied using numerical simulations. By tuning the commensurate fractional-order, the proposed system displays a wide variety of dynamical behaviors ranging from coexistence of quasiperiodic and chaotic attractors and bistable chaotic attractors to point attractor via transient chaos.

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A new 4-D hyperchaotic hidden attractor system: Its dynamics, coexisting attractors, synchronization and microcontroller implementation

International Journal of Electrical and Computer Engineering (IJECE) ◽

10.11591/ijece.v11i3.pp2068-2078 ◽

2021 ◽

Vol 11 (3) ◽

pp. 2068

Author(s):

Basil H. Jasim ◽

Kadhim H. Hassan ◽

Khulood Moosa Omran

Keyword(s):

Secure Communication ◽

Communication Systems ◽

Hardware Implementation ◽

Design Procedure ◽

Hyperchaotic System ◽

Hidden Attractor ◽

Matlab Simulation ◽

Coexisting Attractors ◽

Unknown Parameters ◽

Analog Communication

In this paper, a simple 4-dimensional hyperchaotic system is introduced. The proposed system has no equilibria points, so it admits hidden attractor which is an interesting feature of chaotic systems. Another interesting feature of the proposed system is the coexisting of attractors where it shows periodic and chaotic coexisting attractors. After introducing the system, the system is analyzed dynamically using numerical and theoretical techniques. In this analysis, Lyapunov exponents and bifurcation diagrams have been used to investigate chaotic and hyperchaotic nature, the ranges of system parameters for different behaviors and the route for chaos and coexisting attractors regions. In the next part of our work, a synchronization control system for two identical systems is designed. The design procedure uses a combination of simple synergetic control with adaptive updating laws to identify the unknown parameters derived basing on Lyapunov theorem. Microcontroller (MCU) based hardware implementation system is proposed and tested by using MATLAB as a display side. As an application, the designed synchronization system is used as a secure analog communication system. The designed MCU system with MATLAB Simulation is used to validate the designed synchronization and secure communication systems and excellent results have been obtained.

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Symmetric coexisting attractors and extreme multistability in chaotic system

Modern Physics Letters B ◽

10.1142/s0217984921504583 ◽

2021 ◽

pp. 2150458

Author(s):

Xiaoxia Li ◽

Chi Zheng ◽

Xue Wang ◽

Yingzi Cao ◽

Guizhi Xu

Keyword(s):

Chaotic System ◽

Electronic Circuit ◽

Phase Portraits ◽

Hyperchaotic System ◽

Coexisting Attractors ◽

Extreme Multistability ◽

New Chaotic System ◽

Initial States ◽

Parameter Ranges ◽

New System

In this paper, a new four-dimensional (4D) chaotic system with two cubic nonlinear terms is proposed. The most striking feature is that the new system can exhibit completely symmetric coexisting bifurcation behaviors and four symmetric coexisting attractors with the same Lyapunov exponents in all parameter ranges of the system when taking different initial states. Interestingly, these symmetric coexisting attractors can be considered as unusual symmetrical rotational coexisting attractors, which is a very fascinating phenomenon. Furthermore, by using a memristor to replace the coupling resistor of the new system, an interesting 4D memristive hyperchaotic system with one unstable origin is constructed. Of particular surprise is that it can exhibit four groups of extreme multistability phenomenon of infinitely many coexisting attractors of symmetric distribution about the origin. By using phase portraits, Lyapunov exponent spectra, and coexisting bifurcation diagrams, the dynamics of the two systems are fully analyzed and investigated. Finally, the electronic circuit model of the new system is designed for verifying the feasibility of the new chaotic system.

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Dynamic Analysis, Circuit Design, and Synchronization of a Novel 6D Memristive Four-Wing Hyperchaotic System with Multiple Coexisting Attractors

Complexity ◽

10.1155/2020/5904607 ◽

2020 ◽

Vol 2020 ◽

pp. 1-17 ◽

Cited By ~ 13

Author(s):

Fei Yu ◽

Li Liu ◽

Hui Shen ◽

Zinan Zhang ◽

Yuanyuan Huang ◽

...

Keyword(s):

Control Method ◽

Phase Portraits ◽

Hyperchaotic System ◽

The Novel ◽

Coexisting Attractors ◽

Fundamental Properties ◽

Parameter Values ◽

Multiple Coexisting Attractors ◽

Line Equilibrium ◽

Active Control Method

In this work, a novel 6D four-wing hyperchaotic system with a line equilibrium based on a flux-controlled memristor model is proposed. The novel system is inspired from an existing 5D four-wing hyperchaotic system introduced by Zarei (2015). Fundamental properties of the novel system are discussed, and its complex behaviors are characterized using phase portraits, Lyapunov exponential spectrum, bifurcation diagram, and spectral entropy. When a suitable set of parameters are chosen, the system exhibits a rich repertoire of dynamic behaviors including double-period bifurcation of the quasiperiod, a single two-wing, and four-wing chaotic attractors. Further analysis of the novel system shows that the multiple coexisting attractors can be observed with different system parameter values and initial values. Moreover, the feasibility of the proposed mathematical model is also presented by using Multisim simulations based on an electronic analog of the model. Finally, the active control method is used to design the appropriate controller to realize the synchronization between the proposed 6D memristive hyperchaotic system and the 6D hyperchaotic Yang system with different structures. The Routh–Hurwitz criterion is used to prove the rationality of the controller, and the feasibility and effectiveness of the proposed synchronization method are proved by numerical simulations.

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