Hidden hyperchaotic attractors in a new 4D fractional order system and its synchronization

Li, Ke; Cao, Jianxiong; He, Jin–Man

doi:10.1063/1.5136057

Cited by 14 publications

(8 citation statements)

References 35 publications

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“…The parameter switching (PS) algorithm [35][36][37] is a possible way to determine the location of hidden attractors. When other parameters are kept unchanged and the parameter k p is set to 5.3, the corresponding roots of the characteristic equation can be obtained to be λ 1 = −4.76, λ 2 = −1.8325 + 1.8641i, λ 3 = −1.8325 − 1.8641i, λ 4 = −0.1776, λ 5 = −0.0051 + 0.7563i, and λ 6 = −0.0051 − 0.7563i.…”

Section: Presence Of Hidden Attractor and Its Influence On Dynamical ...mentioning

confidence: 99%

Existence of hidden attractors in nonlinear hydro-turbine governing systems and its stability analysis

Zhao

Wei

et al. 2023

Chinese Phys. B

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This paper studies the stability and hidden dynamics of the nonlinear hydro-turbine governing system with an output limiting link. A new six-dimensional system, which exhibits some hidden attractors, is proposed in this work. The parameter switching algorithm is used to numerically study the dynamic behaviors of the system. Moreover,it is investigated that for some parameters the system with a stable equilibrium point can generate strange hidden attractors. A self-excited attractor is also recognized with the change of its parameters. In addition, numerical simulations are carried out to analyze the dynamic behaviors of the proposed system using the Lyapunov exponential spectrums, Lyapunov dimensions, bifurcation diagrams, phase space orbits, and basins of attraction. Consequently, the findings of this work show that the basins of hidden attractors are tiny for which the standard computational procedure for localization is unavailable. These simulation results help to have better understanding of hidden chaotic attractors in higher-dimensional dynamical systems.It is also of great significance to reveal chaotic oscillations such as uncontrolled speed adjustment in the operation of hydropower station due to small changes in initial values.

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Section: Presence Of Hidden Attractor and Its Influence On Dynamical ...mentioning

confidence: 99%

Existence of hidden attractors in nonlinear hydro-turbine governing systems and its stability analysis

Zhao

Wei

et al. 2023

Chinese Phys. B

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“…They are almost evenly distributed between systems of 3 and 4 differential equations resulting in chaotic or hyperchaotic attractors. The proposed fractionalorder systems cover different types of hidden attractors such as: no equilibria (the majority), one or more stable equilibria, a line or infinite number of equilibria, where one of the recent papers proposed three different types [66]. Hidden attractors in fractional-order discrete systems were also presented [67].…”

Section: B Fractional-order Chaotic Systems With Hidden Attractorsmentioning

confidence: 99%

Self-Reproducing Hidden Attractors in Fractional-Order Chaotic Systems Using Affine Transformations

Sayed

Radwan

2020

IEEE Open J. Circuits Syst.

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This article proposes a unified approach for hidden attractors control in fractional-order chaotic systems. Hidden attractors have small basins of attractions and are very sensitive to initial conditions and parameters. That is, they can be easily drifted from chaotic behavior into another type of dynamics, which is not suitable for encryption applications that require quite wide initial conditions and parameters ranges for encryption key design. Hence, a systematic coordinate affine transformation framework is utilized to construct transformed systems with self-reproducing attractors. Simulation results of two three-dimensional fractional-order chaotic systems with hidden attractors validate that the proposed framework supports attractors geometric structure design and multi-wing generation. Hidden attractor size, polarity, phase, shape and position control while preserving the chaotic dynamics is indicated by strange attractors, spectral entropy, maximum Lyapunov exponent and bifurcation diagrams. Simulations demonstrate the capability of multi-wing generation from fractional-order hidden attractors with no equilibria using non-autonomous parameters as opposed to the classical equilibria extension techniques suitable only for self-excited attractors. The self-reproduced multiple wings can share the same center point or be distributed along an arbitrary line, curve or surface thanks to the non-autonomous translation parameters. Multi-wing attractors widen the basin of attraction and enlarge the state space volume. For practical applications, the proposed technique makes fractional-order systems with hidden attractors suitable for circuit implementations that require specific signal level and polarity conditions. In addition, for digital encryption applications, the relatively wide range of the extra parameters enhances the key space and hence the robustness against brute force attacks.

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“…For example, hyperchaos could help us build better quantum computer [6] and also can make information more secure [7][8][9]. Hyperchaos has also become a hot topic in nonlinear sciences research, see [10][11][12] as well as their references. In addition, as far as we know, the complexity of the hyperchaotic system dynamics has not been completely mastered by researchers until now.…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of a new 5D hyperchaotic system

Li,

Cui

2023

Phys. Scr.

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This paper reports a new five-dimensional (5D) autonomous hyperchaotic system that is obtained by introducing two linear controllers to the Rabinovich system. The dynamical behaviors, including the boundedness, dissipativity and invariance, existence and stability of nonzero equilibrium points are studied and analyzed. The existences of the hyperchaotic and chaotic attractors are numerically verified through analyzing phase trajectories, Lyapunov exponent spectrum, bifurcations and Poincar'{e} maps. The results indicate that the new 5D Rabinovich system can exhibit rich and complex dynamical behaviors. Finally, the existence of Hopf bifurcation, the stability and expression of the Hopf bifurcation are investigated by using the normal form theory and symbolic computations. Some cases are employed to test and verify the theoretical results.

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Hidden hyperchaotic attractors in a new 4D fractional order system and its synchronization

Cited by 14 publications

References 35 publications

Existence of hidden attractors in nonlinear hydro-turbine governing systems and its stability analysis

Existence of hidden attractors in nonlinear hydro-turbine governing systems and its stability analysis

Self-Reproducing Hidden Attractors in Fractional-Order Chaotic Systems Using Affine Transformations

Dynamical analysis of a new 5D hyperchaotic system

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