Search Results (52)

In resource-constrained communication environments, important image data needs to be compressed before encrypted transmission. This paper proposes effective solutions to this issue. Firstly, a new one-dimensional discrete chaotic system model was constructed based on the logistic system and fractional structure. Through theoretical analysis combined with numerical simulation experiments, it has been proven that the proposed new system has excellent chaotic characteristics. Compared with some traditional one-dimensional chaotic systems, the new system has a wider range of chaotic parameters and stronger complexity, making it more suitable for image data encryption. Secondly, a high-compression-ratio image compression method based on improved lifting wavelet transform and a fast image encryption algorithm based on the new chaotic map are proposed. Simulation experiments and security analysis results show that the proposed image compression–encryption scheme has excellent performance and less time overhead. It has good resistance to various cryptanalysis attacks and strong robustness to noise and data loss attacks, which indicates that the proposed image compression–encryption scheme has good application potential in resource-constrained communication environments. The main contribution of this article is the design of a new chaotic system model with practical performance and the development of a new application case. The main novelty of this paper is the proposal of a fast algorithm for high compression ratio and encryption of images. Full article

Accurately identifying damage in beam structures remains a tough challenge, the global trend of wavelet coefficients easily swallows faint local defect signatures, and high-dimensional model updating is computationally inefficient. To tackle these problems, this paper introduces a robust two-stage framework for damage identification that combines a residual-based wavelet strategy with an Improved t-distribution Dung Beetle Optimizer (ITDBO). Rather than relying on guesswork for wavelet selection, we introduce the Residual-based Wavelet Contrast Index (RWCI). By actively stripping away the global trend embedded within the wavelet coefficients, RWCI isolates the pure residual data, drastically amplifying the contrast between genuine stiffness loss and ambient noise for precise damage localization. With the search zone narrowed down, we deploy the ITDBO to quantify the severity. Powered by Bernoulli chaotic mapping and a t-distribution perturbation mechanism, ITDBO effectively bypasses the curse of dimensionality and entirely avoids the premature convergence traps that plague standard metaheuristics. Validated through both numerical simulations and physical experiments on a one-dimensional fixed-fixed steel beam, this hybrid approach proves its mettle. The framework not only accurately flags the defects through heavy noise but also locks onto the exact damage severity with unprecedented efficiency and stability. Full article

Chaotic systems serve as fundamental pseudo-random sequence generators in encryption algorithms and play a vital role in communication security. However, most current research still focus on the classical Logistic chaotic map, making it vulnerable to targeted attacks. To address this issue, this paper proposes a general construction method for a class of cubic chaotic maps over the real number field and proves the existence of chaos based on the robust chaos criterion for S-unimodal maps. Furthermore, by integrating the proposed cubic chaotic map with the infinite folding map, a new one-dimensional discrete chaotic map is developed. Dynamical analysis demonstrates that, compared with the infinite folding map and the Logistic map, the newly constructed map exhibits stronger chaotic behavior and more stable complexity, showing superior potential for practical applications in secure communications. Full article

This paper explores the dynamic analogy between the discrete Lorenzian attractor and a modified Kropotov–Pakhomov neural network (MRNN). A one-dimensional peak map is used to extract the successive maxima of the Lorenzian system and preserve the basic properties of the chaotic flow. The MRNN, governed by the Bogdanov–Hebb learning rule with dissipative feedback, is formulated as a discrete nonlinear operator whose parameters can reproduce the same hierarchy of modes as the peak map. It is theoretically shown that the map multiplier and the spectral radius of the monodromy matrix of the MRNN provide equivalent stability conditions. Numerical diagrams confirm the correspondence between the control parameters of the Lorenz model and the network parameters. The results establish the MRNN as a neural emulator of the Lorenz attractor and offer an analysis of self-organization and stability in adaptive neural systems. Full article

Winding numbers are key indices in the depiction, modelling, and testing of dynamical processes. They capture phase progression on closed curves and are robust for quasiperiodic dynamics, but their status for chaotic Poincaré sections is unclear. This study tests whether any non-trivial winding-type index can be extracted from chaotic Poincaré maps using three approaches: (i) phase-angle analysis, (ii) Kabsch optimal-rotation estimation, and (iii) local turning-angle averaging. To benchmark feasibility and error, we compare four systems: the standard circle map, the same circle map embedded on two planar fractal curves (Koch snowflake and Hilbert curve), a quasiperiodic Duffing–van der Pol (DVP) Poincaré map, and a chaotic DVP Poincaré map. For the quasiperiodic map, all methods yield consistent, accurate winding numbers. For the transitional systems (circle map and its fractal embeddings), indices remain non-trivial but more deviated. In stark contrast, chaotic Poincaré maps produce only trivial indices across all methods. These results indicate a crucial fact about the modelling of chaotic Poincaré maps. That is, although being fractal, they are not merely chaotic maps on fractal curves; rather, they reflect a tighter coupling of geometry and dynamics. Practically, the recoverability of a non-trivial winding index offers a simple diagnostic to distinguish quasiperiodicity from chaos in Poincaré data or corresponding models. The constructed chaotic-map-on-fractal systems also act as test-bed models that bridge ideal one-dimensional mappings and realistic two-dimensional Poincaré sections. Full article

Classifying study objects into groups is facilitated by fuzzy classifiers based on a set of rules and membership functions. Typically, the characteristics of the study objects are used to establish the criteria for classification. This work arises from the need to design fuzzy classifiers in contexts where real data is scarce or highly random, proposing a design based on statistics and chaotic maps that simplifies the design process. This study introduces the development of a fuzzy classifier, assuming that three features of the population to be classified are random variables. A Mamdani fuzzy inference system and three pseudorandom number generators based on one-dimensional chaotic maps are utilized to achieve this. The logistic, Bernoulli, and tent chaotic maps are implemented to emulate the random features of the target population, and their statistical distribution functions serve as input to the fuzzy inference system. Four experimental tests were conducted to demonstrate the functionality of the proposed classifier. The results show that it is possible to achieve a symmetric and robust classification through simple adjustments to membership functions, without the need for supervised training, which represents a significant methodological contribution, especially because this indicates that designers with minimal experience can build effective classifiers in just a few steps. Real applications of the proposed design may focus on the classification of biomedical signals (sEMG), network traffic, and personalized medical assistance systems, where data exhibits high variability and randomness. Full article

We present a novel and completely deterministic method to model chaotic orbits in nonlinear discrete dynamics, taking the quadratic map as an example. This method is based on the resurgent analysis developed by Écalle to perform the resummation of divergent power series given by asymptotic expansions in linear differential equations with variable coefficients. To determine the long-term behavior of the dynamics, we calculate the zeros of a function representing the unstable manifold of the system using Newton’s method. The asymptotic expansion of the function is expressed as a kind of negative power series, which enables the computation with high accuracy. By use of the obtained zeros, we visualize the set of homoclinic points. This set corresponds to the Julia set in one-dimensional complex dynamical systems. The presented method is easily extendable to two-dimensional nonlinear dynamical systems such as Hénon maps. Full article

In this paper, an exponential delay feedback method is proposed to improve the performance of the digital chaotic maps against their dynamical degradation. In this paper, the performance of the scheme is verified using one-dimensional linear, exponential, and nonlinear exponential, Logistic, and Chebyshev maps, and numerical analyses show that the period during which the chaotic sequence enters the cycle is considerably prolonged, and the correlation performance is improved. At the same time, in order to verify the practicality of the method, an image encryption algorithm is designed, and its security analysis results show that the algorithm has a high level of security and can compete with other encryption schemes. Therefore, the exponential delay feedback method can effectively improve the dynamics degradation of a digital chaotic map. Full article

This study presents a novel encryption method for RGB (Red–Green–Blue) color images that combines scrambling techniques with the logistic map equation. In this method, image scrambling serves as a reversible transformation, rendering the image unintelligible to unauthorized users and thus enhancing security against potential attacks. The proposed encryption scheme, called Bit-Plane Representation of Quantum Images (BRQI), utilizes quantum operations in conjunction with a one-dimensional chaotic system to increase encryption efficiency. The encryption algorithm operates in two phases: first, the quantum image undergoes scrambling through bit-plane manipulation, and second, the scrambled image is mixed with a key image generated using the logistic map. To assess the performance of the algorithm, simulations and analyses were conducted, evaluating parameters such as entropy (a measure of disorder) and correlation coefficients to confirm the effectiveness and robustness of this algorithm in safeguarding and encoding color images. The results show that the proposed quantum color image encryption algorithm surpasses classical methods in terms of security, robustness, and computational complexity. Full article

Stream ciphers are a type of symmetric encryption algorithm, and excel in speed and efficiency compared with block ciphers. They are applied in various applications, particularly in digital communications and real-time transmissions. In this paper, we propose lightweight chaotic keystream generators that utilize original one-dimensional (1D) chaotic maps with a counter to fit the requirement of a stream cipher for secure communications in the Internet of Things (IoT). The proposed chaotic scheme, referred to as expanded chaos, improves the limit of the chaotic range for the original 1D chaos. It can resist brute-force attacks, chosen-ciphertext attacks, guess-and-determine attacks, and other known attacks. We implement the proposed scheme on the IoT platform Raspberry Pi. Under NIST SP800-22 tests, the pass rates for the proposed improved chaotic maps with a counter and the proposed the mutual-coupled chaos are found to be at least about 90% and 92%, respectively. Full article

Rigged Hilbert spaces (RHSs) are the right mathematical context that include many tools used in quantum physics, or even in some chaotic classical systems. It is particularly interesting that in RHS, discrete and continuous bases, as well as an abstract basis and the basis of special functions and representations of Lie algebras of symmetries are used by continuous operators. This is not possible in Hilbert spaces. In the present paper, we study a model showing all these features, based on the one-dimensional Pöschl–Teller Hamiltonian. Also, RHS supports representations of all kinds of ladder operators as continuous mappings. We give an interesting example based on one-dimensional Hamiltonians with an infinite chain of SUSY partners, in which the factorization of Hamiltonians by continuous operators on RHS plays a crucial role. Full article

To address the problems of limited population diversity and a tendency to converge prematurely to local optima in the original sparrow search algorithm (SSA), an improved sparrow search algorithm (ISSA) based on multi-strategy collaborative optimization is proposed. ISSA employs three strategies to enhance performance: introducing one-dimensional composite chaotic mapping SPM to generate the initial sparrow population, thus enriching population diversity; introducing the dung beetle dancing search behavior strategy to strengthen the algorithm’s ability to jump out of local optima; integrating the adaptive t-variation improvement strategy to balance global exploration and local exploitation capabilities. Through experiments with 23 benchmark test functions and comparison with algorithms such as PSO, GWO, WOA, and SSA, the advantages of ISSA in convergence speed and optimization accuracy are verified. In the application of robot path planning, compared with SSA, ISSA exhibits shorter path lengths, fewer turnings, and higher planning efficiency in both single-target point and multi-target point path planning. Especially in multi-target point path planning, as the obstacle rate increases, ISSA can more effectively find the shortest path. Its traversal order is different from that of SSA, making the planned path smoother and with fewer intersections. The results show that ISSA has significant superiority in both algorithm performance and path planning applications. Full article

In contemporary wildlife conservation, drones have become essential for the non-invasive monitoring of animal populations and habitats. However, the sensitive data captured by drones, including images and videos, require robust encryption to prevent unauthorized access and exploitation. This paper presents a novel encryption algorithm designed specifically for safeguarding wildlife data. The proposed approach integrates one-dimensional and two-dimensional memory cellular automata (1D MCA and 2D MCA) with a bitwise XOR operation as an intermediate confusion layer. The 2D MCA, guided by chaotic rules from the sine-exponential (SE) map, utilizes varying neighbor configurations to enhance both diffusion and confusion, making the encryption more resilient to attacks. A final layer of 1D MCA, controlled by pseudo-random number generators, ensures comprehensive diffusion and confusion across the image. The SHA-256 hash of the input image is used to derive encryption parameters, providing resistance against plaintext attacks. Extensive performance evaluations demonstrate the effectiveness of the proposed scheme, which balances security and complexity while outperforming existing algorithms. Full article

Certain methods for implementing chaotic maps can lead to dynamic degradation of the generated number sequences. To solve such a problem, we develop a method for generating pseudorandom number sequences based on multiple one-dimensional chaotic maps. In particular, we introduce a Bernoulli chaotic map that utilizes function transformations and constraints on its control parameter, covering complementary regions of the phase space. This approach allows the generation of chaotic number sequences with a wide coverage of phase space, thereby increasing the uncertainty in the number sequence generation process. Moreover, by incorporating a scaling factor and a sine function, we develop a robust chaotic map, called the Sine-Multiple Modified Bernoulli Chaotic Map (SM-MBCM), which ensures a high degree of randomness, validated through statistical mechanics analysis tools. Using the SM-MBCM, we propose a chaotic PRNG (CPRNG) and evaluate its quality through correlation coefficient analysis, key sensitivity tests, statistical and entropy analysis, key space evaluation, linear complexity analysis, and performance tests. Furthermore, we present an FPGA-based implementation scheme that leverages equivalent MBCM variants to optimize the electronic implementation process. Finally, we compare the proposed system with existing designs in terms of throughput and key space. Full article

Due to the security weaknesses of chaos-based pseudorandom number generators, in this paper, a new pseudorandom number generator (PRNG) based on mixing three-dimensional variables of a cat chaotic map is proposed. A uniformly distributed chaotic sequence by a logistic map is used in the mixing step. Both statistical tests and a security analysis indicate that our PRNG has good randomness and is more complex than any one-dimensional variable of a cat map. Furthermore, a new image encryption algorithm based on the chaotic PRNG is provided to protect the content of artwork images. The core of the algorithm is to use the sequence generated by the pseudorandom number generator to achieve the process of disruption and diffusion of the image pixels, so as to achieve the effect of obfuscation and encryption of the image content. Several security tests demonstrate that this image encryption algorithm has a high security level. Full article