A class of two-dimensional rational maps with self-excited and hidden attractors

Zhang, Liping; Liu, Yang; Wei, Zhouchao; Jiang, Haibo; Bi, Qinsheng

doi:10.1088/1674-1056/ac4025

Cited by 5 publications

(4 citation statements)

References 43 publications

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“…In this section, with the help of using the Caputo difference operator Dh g C j , we expand the integer-order twodimensional rational map introduced by Zhang et al [37] to produce the fractional-order discrete-time rational map. In particular, the novel two-dimensional fractional-order discrete-time rational map can be presented by the following equations: a g g b g…”

Section: The Fractional-order Discrete-time Rational Mapmentioning

confidence: 99%

A new two-dimensional fractional discrete rational map: chaos and complexity

Shatnawi¹,

Abbes²,

Ouannas³

et al. 2022

Phys. Scr.

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In this paper, a new two-dimensional fractional discrete rational map with γth-Caputo fractional difference operator is introduced. The study of the presence and stability of the equilibrium points shows that there are four types of equilibrium points; no equilibrium point, a line of equilibrium points, one equilibrium point and two equilibrium points. In addition, in the context of the commensurate and incommensurate instances, the nonlinear dynamics of the suggested fractional discrete map in different cases of equilibrium points are investigated through several numerical techniques including Lyapunov exponents, phase attractors and bifurcation diagrams. These dynamic behaviors suggest that the fractional discrete rational map has both hidden and self-excited attractors, which have rarely been described in the literature. Finally, to validate the presence of chaos, a complexity analysis is carried out using approximation entropy (ApEn) and the C0-measure.

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Section: The Fractional-order Discrete-time Rational Mapmentioning

confidence: 99%

A new two-dimensional fractional discrete rational map: chaos and complexity

Shatnawi¹,

Abbes²,

Ouannas³

et al. 2022

Phys. Scr.

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“…At present, the wireless capsule endoscopes available in the market are mainly magnet-controlled (also called magnetron) and of swallowing type, however, these endoscopes are applied for stomach diagnosis or colonoscopy, cannot applied to small-bowel examinations. In order to improve the shortcomings of wireless capsule endoscopes, self-driving methods such as vibro-impact [1,2,3], inchworm locomotion [4,5,6] and spiral navigation systems [7,8,9] have been proposed. Liu and coworkers [1,10,11] have developed a wireless-driven capsule with an internal oscillating mass impacting the capsule shell.…”

Section: Introductionmentioning

confidence: 99%

Multi-objective optimization of a self-propelled capsule for small-bowel endoscopy considering the influence of intestinal environment

Zhu

Liao

Chávez

et al. 2023

Preprint

Self Cite

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This work studies the control optimization of a self-propelled capsule moving in the small intestine for endoscopic diagnosis. For this purpose, we combine an existing capsule model with the intestinal peristalsis and its internal environment in order to gain a better understanding of dynamics of the self-propelled capsule. For the optimization study, a number of different realistic targets are considered, including the capsule's average progression speed, the impact force acting on the small intestine and the capsule's energy consumption. In addition, the uncertainty of the small intestine environment is taking into account by varying its internal radius. In this setting, we develop a multi-objective optimization strategy based on NSGA-II, Monte Carlo, and Six-Sigma algorithms considering both the control and structural model parameters, such as excitation frequency and impact stiffness. The effectiveness of the proposed optimization strategy is demonstrated via extensive numerical simulations with the consideration of a wide range of realistic scenarios.

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“…However, in recent years, many researchers have found a class of system that has only a stable equilibrium point, no equilibrium points, or an infinite number of equilibrium points where chaotic oscillations are still present, [10][11][12][13] for there exist hidden attractors in these systems. [14] The existence of hidden attractors increased the uncertainty of the system, so the system could suddenly switch to unexpected attractors under slight perturbations and such a transition could lead to disastrous consequences. [15,16] An attractor is hidden if its basin of attractions does not intersect with a neighborhood of all equilibrium points (stationary points), otherwise, it is called a self-excited attractor.…”

Section: Introductionmentioning

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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A class of two-dimensional rational maps with self-excited and hidden attractors

Cited by 5 publications

References 43 publications

A new two-dimensional fractional discrete rational map: chaos and complexity

A new two-dimensional fractional discrete rational map: chaos and complexity

Multi-objective optimization of a self-propelled capsule for small-bowel endoscopy considering the influence of intestinal environment

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

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