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result(s) for
"Chaos theory"
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An effective field theory for non-maximal quantum chaos
A
bstract
In non-maximally quantum chaotic systems, the exponential behavior of out-of-time-ordered correlators (OTOCs) results from summing over exchanges of an infinite tower of higher “spin” operators. We construct an effective field theory (EFT) to capture these exchanges in (0 + 1) dimensions. The EFT generalizes the one for maximally chaotic systems, and reduces to it in the limit of maximal chaos. The theory predicts the general structure of OTOCs both at leading order in the 1/
N
expansion (
N
is the number of degrees of freedom), and after resuming over an infinite number of higher order 1/
N
corrections. These general results agree with those previously explicitly obtained in specific models. We also show that the general structure of the EFT can be extracted from the large
q
SYK model.
Journal Article
A novel color image encryption method based on new three-dimensional chaotic mapping and DNA coding
In recent years, the field of information science has seen a surge in research focused on digital image security. Chaotic systems have emerged as essential tools in the development of image encryption algorithms due to their unpredictability and sensitivity to initial values. In this paper, a novel three-dimensional chaotic system is proposed and its chaotic behavior is validated through an analysis of dissipative properties, phase diagrams, spectral entropy, Lyapunov indices, etc., and more. Leveraging chaotic mapping, a color image encryption algorithm utilizing rotational arithmetic element shuffling and DNA coding is proposed and executed. Validation through simulation experiments and numerical analyses demonstrates the algorithm’s reliability and security.
Journal Article
A novel multi-layer image encryption algorithm based on 2D drop-wave function
Image encryption is an effective method for protecting the security of image information, and chaotic maps are generally applied to realize some random operations. Inspired by the nonlinear characteristic of optimization test functions, a chaotic map called drop-wave map developed from the two-dimensional (2D) drop-wave function is proposed in this paper. The drop-wave map has a wide range of parameters and uniform phase trajectories. Utilizing the generated pseudo-random sequences with the proposed drop-wave map, a novel multi-layer image encryption algorithm is presented through processing bit-planes using bit circle-shift, bit-plane permutation using Baker map, intra-layer permutation, and multi-direction diffusion. First, the bit circle-shift operation is performed on each pixel to change values initially, where the shifted digits are determined with one pseudo-random sequence. Second, the Baker map is used to scramble the bit positions in each bit-plane and the timestamp is regarded as an extra key. Furthermore, the intra-layer permutation operation with another pseudo-random sequence is performed to permutate the bit positions completely. Finally, the ciphertext image is obtained by using multi-direction diffusion to change pixel values. The main contributions of this work lie in the design of a 2D drop-wave map and a combination of multi-layer operations to enhance the security of image encryption. Simulation results and security analysis verify the validity and feasibility of the proposed algorithm through statistical analysis and robustness analysis.
Journal Article
State-extension modulation yields infinite attractors
Initial condition-related coexisting behavior is one of the significant features of specific chaotic systems, which corresponds to the complicated coexistences of multiple attractors or infinite attractors. To modulate the three outputs of the Chua’s system to generate infinite attractors, this paper proposes a state-extension approach via introducing the three outputs to extra dimensions through a simple integral without or with self-feedback. In comparison with most existing initial condition-controlled offset-boostable systems with discontinuous step-boost-type coexisting attractors, this approach has two important features, i.e., the seed Chua’s system is kept unchanged, and infinite continuous offset-boosted attractors or infinite continuous space-scaled attractors can be generated via configuring different initial conditions of the extra introduced variables. Both numerical study and circuit simulation confirmed the feasibility of the design.
Journal Article
High robustness image encryption scheme utilizing memristive hyperchaotic map and Manhattan distance
The popularity of UAVs in various fields has led to the proliferation of images, and the need for information security to protect these images is increasing. This paper proposes a unique highly robustness image encryption scheme founded upon a memristor enhanced Hénon map, designated as 3D-IHM. The proposed 3D-IHM is a hyperchaotic system that exhibits superior chaotic properties and initial value sensitivity, as evidenced by several performance tests. This makes it particularly suitable for image encryption applications. The encryption algorithm utilises the Manhattan distance as the basis for grouping image pixels, and the subsequent Manhattan distance permutation and diffusion can hide the image information well. Performance analysis shows that the obtained
NPCR
and
UACI
scores can pass the strict significance test. Robustness analysis shows that the algorithm can withstand different types and degrees of noise estimation, and even if 15% of the ciphertext data is lost, it is still capable of recovering the majority of the image information from the reconstructed image. Furthermore, the algorithm demonstrates superior performance in terms of encryption efficiency when compared to some of the most advanced algorithms currently in use.
Journal Article
Analysis of influence of thermal tooth backlash on nonlinear dynamic characteristics of planetary gear system
A thermal tooth backlash model of a planetary gear system, which includes the effects of thermal deformation and thermal elastohydrodynamic lubrication film, was established. The variation laws of tooth backlash under variable speed, variable torque, and constant power conditions, as well as the nonlinear dynamic characteristics of the system were analyzed. The results showed that the change in tooth backlash is greatly influenced by thermal deformation numerically, while the thermal elastohydrodynamic lubrication film affects the trend of tooth backlash along the meshing line direction. Combining bifurcation diagrams, Largest Lyapunov exponent plots, poincaré sections, phase portraits, and frequency spectra analysis reveals that under variable speed and constant power conditions, the presence of thermal tooth backlash reduces the chaotic range of the system and transforms some unstable motion states into more stable ones. However, for variable torque conditions, the influence of thermal tooth backlash on the system is more complex with both stable and unstable situations coexisting. This study provides a theoretical basis for selecting backlash parameters in planetary gear system design and avoiding chaotic responses.
Journal Article
Resonance and chaos analysis of fractional-order nonlinear systems with Rayleigh–Duffing terms
In this paper, the bifurcation, vibrational resonance and chaotic motion of a fractional-order dual-frequency system with Rayleigh–Duffing term are studied. Firstly, by using the separation of fast and slow variables, the theoretical expression of the response amplitude of the system at high frequency is obtained. According to the change of the equivalent equilibrium point, we analyze the bifurcation phenomenon of the system, discuss the bistable and monostable resonances of the system under different parameter values, and analyze the influence of the parameter changes on the resonance phenomenon in detail. Then, by extending the Melnikov method to the case of dual-frequency external forces, the critical value of chaos in the system is determined according to the dual-frequency Melnikov theory process of the system, and the criterion of safety basin erosion is obtained. The time history diagram, phase diagram, Poincare cross-section diagram and Lyapunov index were used for numerical verification. Finally, numerical simulation simulates the erosion phenomenon of the safety basin under different parameter changes, and further verifies the correctness of the analysis results.
Journal Article
Reducible-dimension discrete memristive chaotic map
As research on chaotic maps based on discrete memristors advances, the chaotic map of multiple discrete memristors is gradually receiving attention. Therefore, this paper focuses on the parallel structure of multiple memristors and proposes a dimension-reduction method for such systems. The theoretical analysis of this method is validated by a novel reducible-dimension chaotic map based on the parallel structure of dual memristors. Numerical analysis reveals its reducible-dimension characteristics, two-dimensional degenerate attractor, and super-extreme multistability. Moreover, a pseudo-random number generator (PRNG) is designed using the map and the NIST SP800-22 test results show that the generated pseudo-random numbers have high randomness. The physical feasibility of the map is verified using the STM32 platform. Finally, an encryption strategy is proposed based on the degeneracy of this map, and multiple testing methods have verified the superior performance of the encryption system.
Journal Article
An n-dimensional discrete attractor with sinusoidal waveform
Chaos is a rather unique phenomenon caused by nonlinear effects, with characteristics such as sensitivity to initial values, no periodicity, long-term unpredictability, fractal nature, and universality. Attractors are an important component in chaos theory. Different attractor shapes affect the complexity, periodicity and other properties of chaotic systems. This paper proposes a new n-dimensional discrete chaotic system construction scheme, which can generate chaotic attractors with sine wave shapes. In terms of system dynamics, the fixed point of the new system under different parameter values was analyzed. Taking 2-, 3-, and 4-dimensional discrete chaotic systems with sinusoidal waveforms as examples, phase space diagram analysis shows that they can indeed produce obvious sinusoidal wave attractors. Prove the irregularity of chaotic sequences through time series diagrams and spectrograms. Calculating the Lyapunov exponent in each dimension proves that the system is in a chaotic state. This paper also analyzes the chaotic state of the chaotic system under various parameter values through bifurcation diagrams, Lyapunov index diagrams, and demonstrates the relationship between the chaotic state of the system and the variation of the system parameters, and clarifies the parameter values of the system.
Journal Article