Dynamics Analysis and Synchronous Control of Fractional-Order Entanglement Symmetrical Chaotic Systems

Lei, Tengfei; Bei-xing, Mao; Zhou, Xuejiao; Fu, Haiyan

doi:10.3390/sym13111996

Cited by 9 publications

(11 citation statements)

References 35 publications

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“…System (6) is chaos; the maximum Lyapunov exponent is greater than 0, and the C0 and SE complexity is high, as shown in Figure 5c,d. a ∈ [8,12]. At some points in this interval, the system has three positive Lyapunov exponents, at which time the system complexity reaches the maximum, as shown in Figure 5b-d.…”

Section: Parameter a Varyingmentioning

confidence: 94%

“…Fixing the parameters a = 10, b = 8 3 , c = 28, d = −1.3, h = 1.78, k 1 = 1, k 2 = 4.8, take step h as 0.01 and sequence N as 9000. Let the initial value (x 0 , y 0 , z 0 , w 0, u 0 ) = (1, 0.2, 0.3, 0.4, 0.5).…”

Section: Varying Parameter Qmentioning

confidence: 99%

“…In addition, the system complexity is also related to the number of positive Lyapunov exponents. From the bifurcation diagram, it can be seen that the system (6) is periodic under parameter a ∈ [5,8), and the maximum Lyapunov exponent of the corresponding system ( 6) is equal to 0. a ∈ [8,12]. System (6) is chaos; the maximum Lyapunov exponent is greater than 0, and the C0 and SE complexity is high, as shown in Figure 5c,d.…”

Section: Parameter a Varyingmentioning

confidence: 99%

“…Many scholars have found that the fractional-order model is closer to the actual engineering model than the integer-order calculus model. In the aspect of combining fractional-order systems with nonlinear chaotic systems, many scholars have proposed many fractional-order chaotic systems, such as fractional-order Lorenz chaotic or hyperchaotic systems [5,6], fractional-order chaotic systems with line equilibrium [7], fractional-order entanglement chaotic systems [8], and so on [9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

“…[7] used an ADM algorithm to analyze the complexity and dynamic behavior of a fractional-order chaotic system with line equilibrium, and ref. [8] analyzed the dynamics and synchronization control of a fractional-order entangled system. Ref.…”

Section: Introductionmentioning

confidence: 99%

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Adomian Decomposition, Dynamic Analysis and Circuit Implementation of a 5D Fractional-Order Hyperchaotic System

Lei

2022

Symmetry

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In this paper, a class of fractional-order symmetric hyperchaotic systems is studied based on the Adomian decomposition method. Starting from the definition of Adomian, the nonlinear term of a fractional-order five-dimensional chaotic system is decomposed. At the same time, the dynamic behavior of a fractional-order hyperchaotic system is analyzed by using bifurcation diagrams, Lyapunov exponent spectrum, complexity and attractor phase diagrams. The simulation results show that with the decrease of fractional order q, the complexity of the hyperchaotic system increases. Finally, based on the fractional-order circuit design principle, a circuit diagram of the system is designed, and the circuit is simulated by Multisim. The results are consistent with the numerical simulation results, which show that the system can be realized, which provides a foundation for the engineering applications of fractional-order hyperchaotic systems.

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Section: Parameter a Varyingmentioning

confidence: 94%

Section: Varying Parameter Qmentioning

confidence: 99%

Section: Parameter a Varyingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Adomian Decomposition, Dynamic Analysis and Circuit Implementation of a 5D Fractional-Order Hyperchaotic System

Lei

2022

Symmetry

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A novel entanglement functions-based 4D fractional-order chaotic system and its bifurcation analysis

Tang,

Li,

Huang

2024

Phys. Scr.

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A novel 4D fractional-order chaotic entanglement system based on sinusoidal functions is established in this paper. We aim to reveal the relationship between the dynamical behavior of the new system and its entanglement coefficients. It is found that the equilibrium point of the system varies regularly with the successive change of the entanglement coefficient. The supercritical pitchfork bifurcation phenomenon of the new system is discussed based on the fractional-order stability theory. Furthermore, sufficient conditions and threshold for supercritical Hopf bifurcation caused by the entanglement coefficient are provided. Finally, the route to chaos of the new system is explored utilizing multiple numerical indicators, such as spectral entropy complexity, bifurcation diagrams, Lyapunov exponential spectrum, phase portraits, and 0-1 test curves. The results indicate that in addition to various chaotic attractors, there are phenomena such as period-doubling bifurcations, period windows, and coexisting symmetric attractors (periodic or chaotic).

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Cap like trajectories in 5D chaotic tangent hyperbolic memristive model: fractional calculus and encryption

Qureshi,

Alam Khan,

Raza

et al. 2024

Phys. Scr.

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This research aims to investigate the influence of model parameters and fractional order on a novel mathematical model with tangent hyperbolic memristor. This investigation conducted by applying Lyapunov exponents and bifurcation analysis. We utilize the Lyapunov exponent theory to understand and characterize these chaotic behaviors under fractional indices. The Lyapunov exponent, bifurcation, and phase diagrams have been depicted to explore the intricate dynamics of the chaotic system governed by the chaotic equation. This investigation reveals that the system exhibits a wealth of complex behaviors influenced by the system parameters and the order of the fractional derivative. A novel approach termed Atangana-Baleanu-Caputo (ABC) fractional derivative (FD) to generate phase portraits and gain insights into the system's behavior. The random numbers generated by the chaotic system are employed to distort the image through an amalgamated image encryption (AIE) technique. Subsequently, the integrity of the scrambled image has been assessed using various image security evaluation methods to reinforce the notion that combining the chaotic system and image can constitute a valuable encryption key. Finally, the chaotic model circuit realization uses active and passive components, and the outcomes are compared with the numerical simulations.

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Dynamics Analysis and Synchronous Control of Fractional-Order Entanglement Symmetrical Chaotic Systems

Cited by 9 publications

References 35 publications

Adomian Decomposition, Dynamic Analysis and Circuit Implementation of a 5D Fractional-Order Hyperchaotic System

Adomian Decomposition, Dynamic Analysis and Circuit Implementation of a 5D Fractional-Order Hyperchaotic System

A novel entanglement functions-based 4D fractional-order chaotic system and its bifurcation analysis

Cap like trajectories in 5D chaotic tangent hyperbolic memristive model: fractional calculus and encryption

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