Four-wing Hyperchaotic Attractor Research Articles

A no-equilibrium memristive system with four-wing hyperchaotic attractor

A new memristive system is proposed in this paper which can have no equilibrium and a line of equilibrium based on the value of its controlling parameter. Also, changing that parameter can cause the system having both chaotic and hyperchaotic solutions. This system has a multi-wing strange attractor. Dynamical properties of this system such as Lyapunov exponents and bifurcation diagram are calculated. This system belongs to the category of systems with hidden and multistable attractors. A system with all the above-mentioned properties is not common in the literature. Finally, an adaptive sliding mode control method is applied to synchronize this chaotic system.

Generating Four-Wing Hyperchaotic Attractor and Two-Wing, Three-Wing, and Four-Wing Chaotic Attractors in 4D Memristive System

By adding only one smooth flux-controlled memristor into a three-dimensional (3D) pseudo four-wing chaotic system, a new real four-wing hyperchaotic system is constructed in this paper. It is interesting to see that this new memristive chaotic system can generate a four-wing hyperchaotic attractor with a line of equilibria. Moreover, it can generate two-, three- and four-wing chaotic attractors with the variation of a single parameter which denotes the strength of the memristor. At the same time, various coexisting multiple attractors (e.g. three-wing attractors, four-wing attractors and attractors with state transition under the same system parameters) are observed in this system, which means that extreme multistability arises. The complex dynamical behaviors of the proposed system are analyzed by Lyapunov exponents (LEs), phase portraits, Poincaré maps, and time series. An electronic circuit is finally designed to implement the hyperchaotic memristive system.

A four-wing hyper-chaotic attractor generated from a 4-D memristive system with a line equilibrium

A new hyper-chaotic system is presented in this paper by adding a smooth flux-controlled memristor and a cross-product item into a three-dimensional autonomous chaotic system. It is exciting that this new memristive system can show a four-wing hyper-chaotic attractor with a line equilibrium. The dynamical behaviors of the proposed system are analyzed by Lyapunov exponents, bifurcation diagram and Poincare maps. Then, by using the topological horseshoe theory and computer-assisted proof, the existence of hyperchaos in the system is verified theoretically. Finally, an electronic circuit is designed to implement the hyper-chaotic memristive system.

Complex dynamics in a 5-D hyper-chaotic attractor with four-wing, one equilibrium and multiple chaotic attractors

In this paper, a new five-dimensional autonomous hyper-chaotic attractor with complex dynamics is introduced. Nonlinear behavior of the proposed system is different with most well-known chaotic and hyper-chaotic attractors and exists interesting aspects in this system. There are eight parameters to control with only one equilibrium point, and the new dynamics can generate four-wing hyper-chaotic and chaotic attractors for some specific parameters and initial conditions. One remarkable feature of the new system is that it can generate double-wing and four-wing smooth chaotic attractors with special appearance. By using the symmetry properties about the coordinates, initial conditions and bifurcation diagrams, many schemes are presented to indicate multi-scroll or multi-wing systems. The phenomenon of multiple attractors is discussed, which means that several attractors created simultaneously from different initial values, and according to this phenomenon, many strange attractors are obtained. Detailed information on the dynamic of the new system is obtained numerically by means of phase portraits, sensitivity to initial conditions, Lyapunov exponents spectrum, bifurcation diagrams and Poincare maps. The stability analysis of the new attractors has been investigated to understand dynamical behaviors nearby equilibrium points.

A Novel Four-Wing Hyperchaotic Complex System and Its Complex Modified Hybrid Projective Synchronization with Different Dimensions

We introduce a new Dadras system with complex variables which can exhibit both four-wing hyperchaotic and chaotic attractors. Some dynamic properties of the system have been described including Lyapunov exponents, fractal dimensions, and Poincaré maps. More importantly, we focus on a new type of synchronization method of modified hybrid project synchronization with complex transformation matrix (CMHPS) for different dimensional hyperchaotic and chaotic complex systems with complex parameters, where the drive and response systems can be asymptotically synchronized up to a desired complex transformation matrix, not a diagonal matrix. Furthermore, CMHPS between the novel hyperchaotic Dadras complex system and other two different dimensional complex chaotic systems is provided as an example to discuss increased order synchronization and reduced order synchronization, respectively. Numerical results verify the feasibility and effectiveness of the presented schemes.

A novel four-dimensional multi-wing hyper-chaotic attractor and its application in image encryption

In this paper, a novel four-dimensional chaotic system for generating multi-wing chaotic attractors is proposed, and chaotic and hyper-chaotic attractors are generated in different parameters. Besides, basic dynamical properties of the chaotic system, such as equilibrium point Poincaré mapping, dissipativity, power spectrum, Lyapunov exponent spectrum, bifurcation diagram are studied numerically and theoretically. An analog oscillator circuit is designed for implementing the four-wing hyper-chaotic attractors, and the hardware circuit experimental results are shown to be in good agreement with the numerical simulation results. Finally, the four-wing hyper-chaotic system is used for hybrid image encryption of physical chaos encryption and advanced encryption standard encryption algorithm. Because physical chaos is adopted in this system, there does not exist a definitive relationship between plaintexts and ciphertexts. And the statistical characteristics of ciphertexts should be better than those of any other encryption system.

Generating variable number of wings from a novel four-dimensional hyperchaotic system with one equilibrium

In this paper, a novel four-dimensional smooth system is presented. What particularly interests us is that the novel multi-wing chaotic system has only one equilibrium point at the origin. Furthermore, the strange phenomenon that different chaotic attractors such as the two-wing, three-wing chaotic attractors and four-wing hyperchaotic attractor could be generated by changing a single system parameter makes this system unique. By applying either analytical or numerical methods, basic properties of the system such as phase portraits, Poincaré mapping, bifurcation diagram and Lyapunov exponents are investigated to observe chaotic motions. The physical existences of the multi-wing chaotic attractors are verified by an electronic circuit.

Dynamical Analysis of a Fractional Order Multi-Wing Hyper-Chaotic System

The dynamic behaviors of fractional-order systems have attracted increasing attentions recently. In this paper, a fractional-order four-wing hyper-chaotic system which has a rich variety of dynamic behaviors is proposed. We numerically study the dynamic behaviors of this fractional-order system with different conditions. Hyper-chaotic behaviors can be found in this system when the order is lower than 3 and four-wing hyper-chaotic attractors similar to integer order system can be generated. The lowest order for Hyper-chaos to exist in this system is 3.6 and the lowest order for chaos to exist in this system is 2.4.

Robust control for fractional-order four-wing hyperchaotic system using LMI

This paper reports a new fractional-order four-dimensional (4D) smooth autonomous system which is special since it can generate a four-wing hyperchaotic attractor but has only one zero equilibrium. The issue of robust control for the fractional-order hyperchaotic system with uncertainties and interference is considered. On the basis of the fractional Lyapunov stability theorem, a linear state feedback controller is derived to guarantee robust Mittag–Leffler stability of the fractional-order hyperchaotic system. The control strength matrix is obtained by solving the linear matrix inequality (LMI). The effectiveness and robustness of the proposed scheme is verified via numerical simulation.

A Novel Four-Wing Hyper-Chaotic System and Its Circuit Implementation

This paper presents a new continuous-time four-dimensional autonomous hyper-chaotic system based on the generalized augmented Lü system. This system can generate a four-wing hyper-chaotic attractor over a large parameter range. It possesses abundant dynamics characteristics. The existence of this hyper-chaotic attractor is verified through theoretical analysis, numerical simulation and circuit implementation.

Four-wing hyperchaotic attractor generated from a new 4D system with one equilibrium and its fractional-order form

In this paper, a new simple 4D smooth autonomous system is proposed, which illustrates two interesting rare phenomena: first, this system can generate a four-wing hyperchaotic and a four-wing chaotic attractor and second, this generation occurs under condition that the system has only one equilibrium point at the origin. The dynamic analysis approach in the paper involves time series, phase portraits, Lyapunov exponents, bifurcation diagram, and Poincare maps, to investigate some basic dynamical behaviors of the proposed 4D system. The physical existence of the four-wing hyperchaotic attractor is verified by an electronic circuit. Finally, it is shown that the fractional-order form of the system can also generate a chaotic four-wing attractor.

Two Hyperchaotic Systems with Four-wing Attractors and Their Synchronization

In this paper, an approach to generate multi-wing attractors in coupled chaotic systems is investigated. By coupling two identical Lu systems, novel four-wing hyperchaotic attractors are generated. In particular, novel four-wing hyperchaotic attractors are also generated by coupling a lorenz system and a Lu system. The paper shows that the equilibria of the proposed systems have certain symmetries with respect to specific coordinate planes. In addition, general hybrid projective dislocated synchronization between the two proposed systems is discussed, and this synchronization is applied to secure communication through chaotic masking, using the chaotic signal to mask a continuous signal and a discrete signal. In consideration of interfering random white noise, analyzes the characteristics of noise and then presents a de-noising method using wavelet transform. Simulation results show that the two systems can realize synchronization, further more, the information signal can be recovered undistorted when applying this method to secure communication.

A four-wing hyper-chaotic attractor and transient chaos generated from a new 4-D quadratic autonomous system

This paper presents a new four-dimensional (4-D) smooth quadratic autonomous chaotic system, which can present periodic orbit, chaos, and hyper-chaos under the conditions on different parameters. Importantly, the system can generate a four-wing hyper-chaotic attractor and a pair of coexistent double-wing hyper-chaotic attractors with two symmetrical initial conditions. Furthermore, a four-wing transient chaos occurs in the system. The dynamic analysis approach- in the paper involves time series, phase portraits, Poincare maps, bifurcation diagrams, and Lyapunov exponents, to investigate some basic dynamical behaviors of the proposed 4-D system.

Multi-wing hyperchaotic attractors from coupled Lorenz systems

This paper illustrates an approach to generate multi-wing attractors in coupled Lorenz systems. In particular, novel four-wing (eight-wing) hyperchaotic attractors are generated by coupling two (three) identical Lorenz systems. The paper shows that the equilibria of the proposed systems have certain symmetries with respect to specific coordinate planes and the eigenvalues of the associated Jacobian matrices exhibit the property of similarity. In analogy with the original Lorenz system, where the two-wings of the butterfly attractor are located around the two equilibria with the unstable pair of complex-conjugate eigenvalues, this paper shows that the four-wings (eight-wings) of these attractors are located around the four (eight) equilibria with two (three) pairs of unstable complex-conjugate eigenvalues.