Analysis for global characteristics of Lyapunov exponents in vehicle plane motion system

Meng, Fanyu; Shi, Shuming; Zhang, Boshi; Bai, Minghui; Nie, Lin

doi:10.1038/s41598-022-13411-x

Cited by 3 publications

(2 citation statements)

References 29 publications

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“…The Lyapunov exponent [21] is a widely used metric for quantifying chaos in a chaotic behavior. It computes the average divergence between two trajectories obtained with two different initial values that are close to each other.…”

Section: A Chaotic Behavior Of Lyapunov Exponent (Le)mentioning

confidence: 99%

Chaotic-Map Based Encryption for 3D Point and 3D Mesh Fog Data in Edge Computing

et al. 2023

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Recent decades have seen dramatic development and adoption of digital technology. This technological advancement generates a large amount of critical data that must be safeguarded. The security of confidential data is one of the primary concerns in fog computing. As a result, achieving a reliable level of security in the fog computing environment is crucial. In this context, 3D point and mesh fog data are becoming increasingly popular among the various types of data stored in the fog. Data encryption using chaotic behavior is one of the preferred research areas due to its unique properties, such as randomness, determinism, sensitivity to initial conditions, and ergodicity. In this paper, we have taken advantage of this chaotic behavior to achieve higher security. This study presents a novel approach for protecting the privacy of 3D point and mesh fog data. Initially, the fog data coordinates are transformed using the sequence generated by the chaotic behavior. Then, bifurcation analysis is used to depict the enhanced scope of the proposed map. The quality of the proposed chaotic system is assessed using metrics such as the Lyapunov exponent and approximate entropy. Results show that the proposed encryption framework performs superior when subjected to brute-force and statistical attacks. Further, the designed framework produces better results than the prior literature.

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Section: A Chaotic Behavior Of Lyapunov Exponent (Le)mentioning

confidence: 99%

Chaotic-Map Based Encryption for 3D Point and 3D Mesh Fog Data in Edge Computing

et al. 2023

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“…The theorem is intuitive, and it is one of the few theorems that can prove whether there exists a limit cycle 1. In order to use this theorem we need to construct a closed region, and it is difficult to construct a closed region that there exists a limit cycle in the region; From the above comparison, we can see that the Lyapunov-LaSalle energy-based analytical method can give quantitative result about the stability of an equilibrium point, and the Lyapunov-LaSalle energy-based approach is applicable to all dynamical systems [77][78][79][80][81][82]. However, in order to use this method, we need to choose the right Lyapunov function, and usually it is difficult to choose the right Lyapunov candidate function.…”

Section: Advantages Disadvantagesmentioning

confidence: 99%

Stability Analysis of Equilibrium Point and Limit Cycle of Two-Dimensional Nonlinear Dynamical Systems—A Tutorial

Wei

2023

Applied Sciences

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The equilibrium state of a dynamical system can be divided into the equilibrium point and limit cycle. In this paper, the stability analysis of the equilibrium point and limit cycle of dynamical systems are presented through different and all possible approaches, and those approaches are compared as well. In particular, the author presented the stability analysis of the equilibrium point through phase plane approach, Lyapunov–LaSalle energy-based approach, and linearization approach, respectively, for two-dimensional nonlinear system, while the stability analysis of the limit cycle is analyzed by using the LaSalle local invariant set theorem and Poincaré–Bendixson theorem, which is only valid in two-dimensional systems. Different case studies are used to demonstrate the stability analysis of equilibrium point and limit cycle.

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Energy harvesting from friction-induced vibrations in vehicle braking systems in the presence of rotary unbalances

Sani,

Balaram,

Kudra

et al. 2024

Energy

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Analysis for global characteristics of Lyapunov exponents in vehicle plane motion system

Cited by 3 publications

References 29 publications

Chaotic-Map Based Encryption for 3D Point and 3D Mesh Fog Data in Edge Computing

Chaotic-Map Based Encryption for 3D Point and 3D Mesh Fog Data in Edge Computing

Stability Analysis of Equilibrium Point and Limit Cycle of Two-Dimensional Nonlinear Dynamical Systems—A Tutorial

Energy harvesting from friction-induced vibrations in vehicle braking systems in the presence of rotary unbalances

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