Hidden Extreme Multistability, Antimonotonicity and Offset Boosting Control in a Novel Fractional-Order Hyperchaotic System Without Equilibrium

Zhang, Sen; Zeng, Yicheng; Li, Zhijun; Zhou, Chengyi

doi:10.1142/s0218127418501675

Cited by 51 publications

(20 citation statements)

References 63 publications

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“…Circuit designs have been used to confirm the realization ability of mathematical models [20][21][22][23][24]. Based on PSIM software, a circuit realization scheme of the commensurate fractional chaotic system with order q � 0.99 and parameters a � 10, b � 40, c � 2.5, k � 1, h � 4, g � 5, d � 20, and m � 1 is designed and implemented.…”

Section: Circuit Implementation Of the Fractional-order Systemmentioning

confidence: 99%

Fractional-Order Hidden Attractor Based on the Extended Liu System

Wang

Liu

Cai

et al. 2020

Mathematical Problems in Engineering

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In this paper, a new commensurate fractional-order chaotic oscillator is presented. The mathematical model with a weak feedback term, which is named hypogenetic flow, is proposed based on the Liu system. And with changing the parameters of the system, the hidden attractor can have no equilibrium points or line equilibrium. What is more interesting is that under the occasion that no equilibrium point can be obtained, the phase trajectory can converge to a minimal field under the lead of some initial conditions, similar to the fixed point. We call it the virtual equilibrium point. On the other hand, when the value of parameters can produce an infinite number of equilibrium points, the line equilibrium points are nonhyperbolic. Moreover than that, there are coexistence attractors, which can present hyperchaos, chaos, period, and virtual equilibrium point. The dynamic characteristics of the system are analyzed, and the parameter estimation is also studied. Then, an electronic circuit implementation of the system is built, which shows the feasibility of the system. At last, for the fractional system with hidden attractors, the finite-time synchronization control of the system is carried out based on the finite-time stability theory of the fractional system. And the effectiveness of the controller is verified by numerical simulation.

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Section: Circuit Implementation Of the Fractional-order Systemmentioning

confidence: 99%

Fractional-Order Hidden Attractor Based on the Extended Liu System

Wang

Liu

Cai

et al. 2020

Mathematical Problems in Engineering

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“…And in Fractional-Order 4D Hyperchaotic Memristive designed by Jun Mou et al, the SE value is about 0.6 [56]. In other chaotic systems, SE is in the range of 0.5-0.8 [57][58][59][60][61][62][63][64][65][66][67][68][69]. Therefore, the high complexity of hiding the chaos using the memristor can provide a safer key for communication, which is of great theoretical significance for the development of chaotic security technology.…”

Section: Se Analysis Depending On Parametersmentioning

confidence: 99%

A High Spectral Entropy (SE) Memristive Hidden Chaotic System with Multi-Type Quasi-Periodic and its Circuit

Liu

Liang

et al. 2019

Entropy

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As a new type of nonlinear electronic component, a memristor can be used in a chaotic system to increase the complexity of the system. In this paper, a flux-controlled memristor is applied to an existing chaotic system, and a novel five-dimensional chaotic system with high complexity and hidden attractors is proposed. Analyzing the nonlinear characteristics of the system, we can find that the system has new chaotic attractors and many novel quasi-periodic limit cycles; the unique attractor structure of the Poincaré map also reflects the complexity and novelty of the hidden attractor for the system; the system has a very high complexity when measured through spectral entropy. In addition, under different initial conditions, the system exhibits the coexistence of chaotic attractors with different topologies, quasi-periodic limit cycles, and chaotic attractors. At the same time, an interesting transient chaos phenomenon, one kind of novel quasi-periodic, and weak chaotic hidden attractors are found. Finally, we realize the memristor model circuit and the proposed chaotic system use off-the-shelf electronic components. The experimental results of the circuit are consistent with the numerical simulation, which shows that the system is physically achievable and provides a new option for the application of memristive chaotic systems.

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“…In [8], Kumar et al constructed a new finance model too, namely, the four-dimensional chaotic financial model and used the Lyapunov direct method to study the stability of the equilibrium points and also proposed the numerical simulations of the new model. For more investigations, like the works proposed by He in [9,10], Yichen and others authors in [11,12], Pham in [13,14], and Shirkavand in [15], see also in [3,5].…”

Section: Introductionmentioning

confidence: 97%

Analysis of a Four-Dimensional Hyperchaotic System Described by the Caputo–Liouville Fractional Derivative

Sene

2020

Complexity

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A new four-dimensional hyperchaotic financial model is introduced. The novelties come from the fractional-order derivative and the use of the quadric function x 4 in modeling accurately the financial market. The existence and uniqueness of its solutions have been investigated to justify the physical adequacy of the model and the numerical scheme proposed in the resolution. We offer a numerical scheme of the new four-dimensional fractional hyperchaotic financial model. We have used the Caputo–Liouville fractional derivative. The problems addressed in this paper have much importance to approach the interest rate, the investment demand, the price exponent, and the average profit margin. The validation of the chaotic, hyperchaotic, and periodic behaviors of the proposed model, the bifurcation diagrams, the Lyapunov exponents, and the stability analysis has been analyzed in detail. The proposed numerical scheme for the hyperchaotic financial model is destined to help the agents decide in the financial market. The solutions of the 4D fractional hyperchaotic financial model have been analyzed, interpreted theoretically, and represented graphically in different contexts. The present paper is mathematical modeling and is a new tool in economics and finance. We also confirm, as announced in the literature, there exist hyperchaotic systems in the fractional context, which admit one positive Lyapunov exponent.

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Hidden Extreme Multistability, Antimonotonicity and Offset Boosting Control in a Novel Fractional-Order Hyperchaotic System Without Equilibrium

Cited by 51 publications

References 63 publications

Fractional-Order Hidden Attractor Based on the Extended Liu System

Fractional-Order Hidden Attractor Based on the Extended Liu System

A High Spectral Entropy (SE) Memristive Hidden Chaotic System with Multi-Type Quasi-Periodic and its Circuit

Analysis of a Four-Dimensional Hyperchaotic System Described by the Caputo–Liouville Fractional Derivative

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