Search Results (93)

Background: Glioblastoma (GBM) is among the most aggressive and morphologically heterogeneous brain tumors. Beyond static imaging biomarkers, its structural organization can be viewed as a nonlinear dynamical system. Characterizing morphodynamic attractors within such a system may reveal latent stability patterns of morphological change and potential indicators of morphodynamic organization. Methods: We analyzed 494 subjects from the multi-institutional BraTS 2020 dataset using a fully automated computational pipeline. Each multimodal MRI volume was encoded into a 16-dimensional latent space using a 3D convolutional autoencoder. Synthetic morphological trajectories, generated through bidirectional growth–shrinkage transformations of tumor masks, enabled training of a contraction-regularized Neural Ordinary Differential Equation (Neural ODE) to model continuous-time latent morphodynamics. Morphological complexity was quantified using fractal dimension (DF), and local dynamical stability was measured via a Lyapunov-like exponent (λ). Robustness analyses assessed the stability of DF–λ regimes under multi-scale perturbations, synthetic-order reversal (directionality; sign-aware comparison) and stochastic noise, including cross-generator generalization against a time-shuffled negative control. Results: The DF–λ morphodynamic phase map revealed three characteristic regimes: (1) stable morphodynamics (λ < 0), associated with compact, smoother boundaries; (2) metastable dynamics (λ ≈ 0), reflecting weakly stable or transitional behavior; and (3) unstable or chaotic dynamics (λ > 0), associated with divergent latent trajectories. Latent-space flow fields exhibited contraction-induced attractor-like basins and smoothly diverging directions. Kernel-density estimation of DF–λ distributions revealed a prominent population cluster within the metastable regime, characterized by moderate-to-high geometric irregularity (DF ≈ 1.85–2.00) and near-neutral dynamical stability (λ ≈ −0.02 to +0.01). Exploratory clinical overlays showed that fractal dimension exhibited a modest negative association with survival, whereas λ did not correlate with clinical outcome, suggesting that the two descriptors capture complementary and clinically distinct aspects of tumor morphology. Conclusions: Glioblastoma morphology can be represented as a continuous dynamical process within a learned latent manifold. Combining Neural ODE–based dynamics, fractal morphometry, and Lyapunov stability provides a principled framework for dynamic radiomics, offering interpretable morphodynamic descriptors that bridge fractal geometry, nonlinear dynamics, and deep learning. Because BraTS is cross-sectional and the synthetic step index does not represent biological time, any clinical interpretation is hypothesis-generating; validation in longitudinal and covariate-rich cohorts is required before prognostic or treatment-monitoring use. The resulting DF–λ morphodynamic map provides a hypothesis-generating morphodynamic representation that should be evaluated in covariate-rich and longitudinal cohorts before any prognostic or treatment-monitoring use. Full article

Amid growing threats of image data leakage and misuse, image encryption has become a critical safeguard for protecting visual information. However, many recent image encryption algorithms remain constrained by trade-offs between security, efficiency, and practicability. To address these challenges, this paper first proposes a novel two-dimensional variable fractional-order coupled quadratic hyperchaotic map (2D-VFCQHM), which incorporates a state-dependent dynamic memory effect, wherein the fractional-order is adaptively determined at each iteration by the mean of the system’s current state. This mechanism substantially enhances the complexity and unpredictability of the underlying chaotic dynamics. Building upon the superior hyperchaotic properties of the 2D-VFCQHM, we further develop a high-performance image encryption algorithm that integrates a novel fusion strategy within a dynamic vector-level diffusion-scrambling framework (IEA-VMFD). Comprehensive security analyses and experimental results demonstrate that the proposed algorithm achieves robust cryptographic performance, including a key space of $2^{298}$, inter-pixel correlation coefficients below 0.0018, ciphertext entropy greater than 7.999, and near-ideal plaintext sensitivity. Crucially, the algorithm attains an encryption speed of up to 126.2963 Mbps. The exceptional balance between security strength and computational efficiency underscores the practical viability of our algorithm, rendering it well-suited for modern applications such as telemedicine, instant messaging, and cloud computing. 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

The study of economic maps has consistently attracted researchers due to their rich dynamics and practical relevance. A deeper understanding of these systems enables the development of more effective control strategies. In this work, we examine the influence of the fractional order $\upsilon$ with the Caputo fractional difference on an economic market map. The primary contribution is the comprehensive analysis of how both commensurate and incommensurate fractional orders affect the stability and complexity of the map. Numerical investigations, including phase portraits, largest Lyapunov exponents, and bifurcation analysis, reveal that the system undergoes a cascade of period-doubling bifurcations before transitioning into chaos. To further characterize the dynamics, complexity is evaluated using the 0–1 test and $C_0$ complexity, both confirming chaotic behavior. Furthermore, two-dimensional control schemes are introduced and theoretically validated to both stabilize the chaotic economic market map and achieve synchronization with a combined response map. The theoretical and numerical results are validated through MATLAB 2016 simulations. Full article

With the rapid advancement of hyperspectral remote sensing technology, the security of hyperspectral images (HSIs) has become a critical concern. However, traditional image encryption methods—designed primarily for grayscale or RGB images—fail to address the high dimensionality, large data volume, and spectral-domain characteristics inherent to HSIs. Existing chaotic encryption schemes often suffer from limited chaotic performance, narrow parameter ranges, and inadequate spectral protection, leaving HSIs vulnerable to spectral feature extraction and statistical attacks. To overcome these limitations, this paper proposes a novel hyperspectral image encryption algorithm based on a newly designed two-dimensional cross-coupled hyperchaotic map (2D-CSCM), which synergistically integrates Cubic, Sinusoidal, and Chebyshev maps. The 2D-CSCM exhibits superior hyperchaotic behavior, including a wider hyperchaotic parameter range, enhanced randomness, and higher complexity, as validated by Lyapunov exponents, sample entropy, and NIST tests. Building on this, a layered encryption framework is introduced: spectral-band scrambling to conceal spectral curves while preserving spatial structure, spatial pixel permutation to disrupt correlation, and a bit-level diffusion mechanism based on dynamic DNA encoding, specifically designed to secure high bit-depth digital number (DN) values (typically >8 bits). Experimental results on multiple HSI datasets demonstrate that the proposed algorithm achieves near-ideal information entropy (up to 15.8107 for 16-bit data), negligible adjacent-pixel correlation (below 0.01), and strong resistance to statistical, cropping, and differential attacks (NPCR ≈ 99.998%, UACI ≈ 33.30%). The algorithm not only ensures comprehensive encryption of both spectral and spatial information but also supports lossless decryption, offering a robust and practical solution for secure storage and transmission of hyperspectral remote sensing imagery. Full article

In recent years, fractional-order controllers have garnered increasing attention due to their enhanced flexibility and superior dynamic performance in control system design. Among them, the fractional-order Proportional–Integral–Derivative (FOPID) controller offers two additional tunable parameters, $\lambda$ and $\mu$, expanding the design space and allowing for finer performance tuning. However, the increased parameter dimensionality poses significant challenges for optimisation. To address this, the present study investigates the application of FOPID controllers to a two-wheeled self-balancing robot (TWSBR), with controller parameters optimised using intelligent algorithms. A novel Multi-Strategy Improved Beluga Whale Optimization (MSBWO) algorithm is proposed, integrating chaotic mapping, elite pooling, adaptive Lévy flight, and a golden sine search mechanism to enhance global convergence and local search capability. Comparative experiments are conducted using several widely known algorithms to evaluate performance. Results demonstrate that the FOPID controller optimised via the proposed MSBWO algorithm significantly outperforms both traditional PID and FOPID controllers tuned by other optimisation strategies, achieving faster convergence, reduced overshoot, and improved stability. 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

This study conducts an in-depth analysis of the dynamical characteristics and solitary wave solutions of the integrable Zhanbota-IIA equation through the lens of planar dynamic system theory. This research applies Lie symmetry to convert nonlinear partial differential equations into ordinary differential equations, enabling the investigation of bifurcation, phase portraits, and dynamic behaviors within the framework of chaos theory. A variety of analytical instruments, such as chaotic attractors, return maps, recurrence plots, Lyapunov exponents, Poincaré maps, three-dimensional phase portraits, time analysis, and two-dimensional phase portraits, are utilized to scrutinize both perturbed and unperturbed systems. Furthermore, the study examines the power frequency response and the system’s sensitivity to temporal delays. A novel classification framework, predicated on Lyapunov exponents, systematically categorizes the system’s behavior across a spectrum of parameters and initial conditions, thereby elucidating aspects of multistability and sensitivity. The perturbed system exhibits chaotic and quasi-periodic dynamics. The research employs the maximum Lyapunov exponent portrait as a tool for assessing system stability and derives solitary wave solutions accompanied by illustrative visualization diagrams. The methodology presented herein possesses significant implications for applications in optical fibers and various other engineering disciplines. Full article

In this study, the key challenges faced by global navigation satellite systems (GNSSs) in the field of security are addressed, and an eye diagram-based deep learning framework for intelligent classification of interference types is proposed. GNSS signals are first transformed into two-dimensional eye diagrams, enabling a novel visual representation wherein interference types are distinguished through entropy-centric feature analysis. Specifically, the quantification of information entropy within these diagrams serves as a theoretical foundation for extracting salient discriminative features, reflecting the structural complexity and uncertainty of the underlying signal distortions. We designed a hybrid architecture that integrates spatial feature extraction, gradient stability enhancement, and time dynamics modeling capabilities and combines the advantages of a convolutional neural network, residual network, and bidirectional long short-term memory network. To further improve model performance, we propose an improved coati optimization algorithm (ICOA), which combines chaotic mapping, an elite perturbation mechanism, and an adaptive weighting strategy for hyperparameter optimization. Compared with mainstream optimization methods, this algorithm improves the convergence accuracy by more than 30%. Experimental results on jamming datasets (continuous wave interference, chirp interference, pulse interference, frequency-modulated interference, amplitude-modulated interference, and spoofing interference) demonstrate that our method achieved performance in terms of accuracy, precision, recall, F1 score, and specificity, with values of 98.02%, 97.09%, 97.24%, 97.14%, and 99.65%, respectively, which represent improvements of 1.98%, 2.80%, 6.10%, 4.59%, and 0.33% over the next-best model. This study provides an efficient, entropy-aware, intelligent, and practically feasible solution for GNSS interference identification. Full article

With the rapid advancement of information technology, as critical information carriers, images are confronted with significant security risks. To ensure the image security, this paper proposes an image encryption algorithm based on a dynamic rhombus transformation and digital tube model. Firstly, a two-dimensional hyper-chaotic system is constructed by combining the Sine map, Cubic map and May map. The analysis results demonstrate that the constructed hybrid chaotic map exhibits superior chaotic characteristics in terms of bifurcation diagrams, Lyapunov exponents, sample entropy, etc. Secondly, a dynamic rhombus transformation is proposed to scramble pixel positions, and chaotic sequences are used to dynamically select transformation centers and traversal orders. Finally, a digital tube model is designed to diffuse pixel values, which utilizes chaotic sequences to dynamically control the bit reversal and circular shift operations, and the exclusive OR operation to diffuse pixel values. The performance analyses show that the information entropy of the cipher image is 7.9993, and the correlation coefficients in horizontal, vertical, and diagonal directions are 0.0008, 0.0001, and 0.0005, respectively. Moreover, the proposed algorithm has strong resistance against noise attacks, cropping attacks, and exhaustive attacks, effectively ensuring the security of images during storage and transmission. Full article

We explore the concept of scaling invariance in a type of dynamical systems that undergo a transition from regularity to chaos. The systems are described by a two-dimensional, nonlinear mapping that preserves the area in the phase space. The key variables are the action and the angle, as usual from Hamiltonian systems. The transition is influenced by a control parameter giving the form of the order parameter. We observe a scaling invariance in the average squared action within the chaotic region, providing evidence that this change from regularity (integrability) to chaos (non-integrability) is akin to a second-order or continuous phase transition. As the order parameter approaches zero, its response against the variation in the control parameter (susceptibility) becomes increasingly pronounced (indeed diverging), resembling a phase transition. Full article

Chaotic systems have demonstrated significant potential in the field of image encryption due to their extreme sensitivity to initial conditions, inherent unpredictability, and pseudo-random behavior. However, existing chaos-based encryption schemes still face several limitations, including narrow chaotic regions, discontinuous chaotic ranges, uneven trajectory distributions, and fixed pixel processing sequences. These issues substantially hinder the security and efficiency of such algorithms. To address these challenges, this paper proposes a novel hyperchaotic map, termed the two-dimensional cross-coupled chaotic map (2D-CFCM), derived from a newly designed 2D cross-coupled chaotic system. The proposed 2D-CFCM exhibits enhanced randomness, greater sensitivity to initial values, a broader chaotic region, and a more uniform trajectory distribution, thereby offering stronger security guarantees for image encryption applications. Based on the 2D-CFCM, an innovative image encryption method was further developed, incorporating efficient scrambling and forward and reverse random multidirectional diffusion operations with symmetrical properties. Through simulation tests on images of varying sizes and resolutions, including color images, the results demonstrate the strong security performance of the proposed method. This method has several remarkable features, including an extremely large key space (greater than $2^{912}$), extremely high key sensitivity, nearly ideal entropy value (greater than 7.997), extremely low pixel correlation (less than 0.04), and excellent resistance to differential attacks (with the average values of NPCR and UACI being $99.6050\%$ and $33.4643\%$, respectively). Compared to existing encryption algorithms, the proposed method provides significantly enhanced security. Full article

As a core component of automated logistics systems, delivery robots hold significant application value in the field of unmanned delivery. This research addresses the robot path planning problem, aiming to enhance delivery efficiency and reduce operational costs through systematic improvements to the RIME optimization algorithm. Through in-depth analysis, we identified several major drawbacks in the standard RIME algorithm for path planning: insufficient global exploration capability in the initial stages, a lack of diversity in the hard RIME search mechanism, and oscillatory phenomena in soft RIME step size adjustment. These issues often lead to undesirable phenomena in path planning, such as local optima traps, path redundancy, or unsmooth trajectories. To address these limitations, this study proposes the Multi-Strategy Controlled Rime Algorithm (MSRIME), whose innovation primarily manifests in three aspects: first, it constructs a multi-strategy collaborative optimization framework, utilizing an infinite folding Fuch chaotic map for intelligent population initialization to significantly enhance the diversity of solutions; second, it designs a cooperative mechanism between a controlled elite strategy and an adaptive search strategy that, through a dynamic control factor, autonomously adjusts the strategy activation probability and adaptation rate, expanding the search space while ensuring algorithmic convergence efficiency; and finally, it introduces a cosine annealing strategy to improve the step size adjustment mechanism, reducing parameter sensitivity and effectively preventing path distortions caused by abrupt step size changes. During the algorithm validation phase, comparative tests were conducted between two groups of algorithms, demonstrating their significant advantages in optimization capability, convergence speed, and stability. Further experimental analysis confirmed that the algorithm’s multi-strategy framework effectively suppresses the impact of coordinate and dimensional differences on path quality during iteration, making it more suitable for delivery robot path planning scenarios. Ultimately, path planning experimental results across various Building Coverage Rate (BCR) maps and diverse application scenarios show that MSRIME exhibits superior performance in key indicators such as path length, running time, and smoothness, providing novel technical insights and practical solutions for the interdisciplinary research between intelligent logistics and computer science. Full article

The deep integration of smart grid and Internet of Things technologies has made high-speed power line carrier communication a key communication technology in energy management, industrial monitoring, and smart home applications, owing to its advantages of requiring no additional wiring and offering wide coverage. However, the inherent characteristics of power line channels, such as strong noise, multipath fading, and time-varying properties, pose challenges to traditional encryption algorithms, including low key distribution efficiency and weak anti-interference capabilities. These issues become particularly pronounced in high-speed transmission scenarios, where the conflict between data security and communication reliability is more acute. To address this problem, a secure transmission method for high-speed power line carrier communication based on generalized two-dimensional polynomial chaotic mapping is proposed. A high-speed power line carrier communication network is established using a power line carrier routing algorithm based on the minimal connected dominating set. The autoregressive moving average model is employed to determine the degree of transmission fluctuation deviation in the high-speed power line carrier communication network. Leveraging the complex dynamic behavior and anti-decoding capability of generalized two-dimensional polynomial chaotic mapping, combined with the deviation, the communication key is generated. This process yields encrypted high-speed power line carrier communication ciphertext that can resist power line noise interference and signal attenuation, thereby enhancing communication confidentiality and stability. By applying reference modulation differential chaotic shift keying and integrating the ciphertext of high-speed power line carrier communication, a secure transmission scheme is designed to achieve secure transmission in high-speed power line carrier communication. The experimental results demonstrate that this method can effectively establish a high-speed power line carrier communication network and encrypt information. The maximum error rate obtained by this method is 0.051, and the minimum error rate is 0.010, confirming its ability to ensure secure transmission in high-speed power line carrier communication while improving communication confidentiality. Full article

To meet the growing demand for secure and reliable image protection in digital communication, this paper proposes a novel image encryption framework that addresses the challenges of high plaintext sensitivity, resistance to statistical attacks, and key security. The method combines a two-dimensional dynamically coupled map lattice (2D DCML) with elementary cellular automata (ECA) to construct a heterogeneous chaotic system with strong spatiotemporal complexity. To further enhance nonlinearity and diffusion, a multi-source perturbation mechanism and adaptive DNA encoding strategy are introduced. These components work together to obscure the image structure, pixel correlations, and histogram characteristics. By embedding spatial and temporal symmetry into the coupled lattice evolution and perturbation processes, the proposed method ensures a more uniform and balanced transformation of image data. Meanwhile, the method enhances the confusion and diffusion effects by utilizing the principle of symmetric perturbation, thereby improving the overall security of the system. Experimental evaluations on standard images demonstrate that the proposed scheme achieves high encryption quality in terms of histogram uniformity, information entropy, NPCR, UACI, and key sensitivity tests. It also shows strong resistance to chosen plaintext attacks, confirming its robustness for secure image transmission. Full article