Intelligent control of convergence rate of impulsive dynamic systems affected by nonlinear disturbances under stabilizing impulses and its application in Chua’s circuit

Wang, Xuezhen; Zhang, Huasheng

doi:10.1016/j.chaos.2023.113289

Cited by 6 publications

(2 citation statements)

References 22 publications

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“…Chaos map often requires a high degree of complexity in practical applications and can achieve it by coupling memristors. So far, continuous memristors have been practiced and applied in many fields [3][4][5][6][7]. Discrete memristor models are easier to implement with digital hardware platforms than continuous memristor models.…”

Section: Introductionmentioning

confidence: 99%

Design and analysis of discrete fractional-order chaotic map with offset-boosting behavior

Huang,

Zheng,

Yang

et al. 2024

Preprint

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This paper presents a 3D discrete fractional-order chaotic map (DFOCM) with offset-boosting behavior based on the memristor. Different from the integer-order chaotic map, the offset-boosting behavior of the DFOCM with parameter offset is associated with the initial value, primarily due to the unique memory properties of fractional-order differences. In addition, rich dynamical properties of the DFOCM are examined using the 0-1 test, maximal Lyapunov exponent, phase diagram, and bifurcation diagram. Numerical simulations show that this DFOCM exhibits more complex dynamical behavior than its integer-order one. Meanwhile, the multistability and conditional symmetry of the DFOCM are studied. The unpredictability and high pseudo-randomness of the chaotic sequence produced by the DFOCM are confirmed by the SE complexity. Finally, the suggested DFOCM is implemented on the DSP hardware platform, demonstrating the physical feasibility of the numerical simulation.

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Section: Introductionmentioning

confidence: 99%

Design and analysis of discrete fractional-order chaotic map with offset-boosting behavior

Huang,

Zheng,

Yang

et al. 2024

Preprint

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“…Beyond the geometrical properties, many of the dynamical systems have chaotic behaviors and are found in practical applications in engineering (e.g., Chua's circuits [16,17], the turbulence in the atmosphere and oceans [18], and plasma control systems [19]) or in medicine (e.g., multi-scale synthesis of Alzheimer's pathogenesis [20], neuroethology [21], and a model of stress as a dynamical system [22]).…”

Section: Introductionmentioning

confidence: 99%

Semi-Analytical Closed-Form Solutions for the Rikitake-Type System through the Optimal Homotopy Perturbation Method

Ene

Pop

2023

Mathematics

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The goal of this work is to build semi-analytical solutions of the Rikitake-type system by means of the optimal homotopy perturbation method (OHPM) using only two iterations. The chaotic behaviors are excepted. By taking into consideration the geometrical properties of the Rikitake-type system, the closed-form solutions can be established. The obtained solutions have a periodical behavior. These geometrical properties allow reducing the initial system to a second-order nonlinear differential equation. The latter equation is solved analytically using the OHPM procedure. The validation of the OHPM method is presented for three cases of the physical parameters. The advantages of the OHPM technique, such as the small number of iterations (the efficiency), the convergence control (in the sense that the semi-analytical solutions are approaching the exact solution), and the writing of the solutions in an effective form, are shown graphically and with tables. The accuracy of the results provides good agreement between the analytical and corresponding numerical results. Other dynamic systems with similar geometrical properties could be successfully solved using the same procedure.

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On the uniqueness of periodic solutions for a Rayleigh–Liénard system with impulses

Chen,

Jin,

Wang

et al. 2024

Math. Ann.

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Intelligent control of convergence rate of impulsive dynamic systems affected by nonlinear disturbances under stabilizing impulses and its application in Chua’s circuit

Cited by 6 publications

References 22 publications

Design and analysis of discrete fractional-order chaotic map with offset-boosting behavior

Design and analysis of discrete fractional-order chaotic map with offset-boosting behavior

Semi-Analytical Closed-Form Solutions for the Rikitake-Type System through the Optimal Homotopy Perturbation Method

On the uniqueness of periodic solutions for a Rayleigh–Liénard system with impulses

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