Chaos最新文献

Higher-order topological features extend conventional graph models by capturing multi-node interactions, enabling more accurate modeling of structural robustness in complex systems. However, understanding the structural influence in complex networks remains challenging, especially when connectivity involves multiple scales and higher-order dependencies. This paper introduces the persistent structural influence indicator, which integrates persistent homology with local geometric perturbation analysis to quantify the node influence by extracting latent higher-order topological features from complex networks. Our model effectively captures multi-scale topological features and localized structural sensitivities, providing orthogonal information to classical centrality measures. Evaluations on both synthetic and real-world networks demonstrate that the proposed model more accurately identifies structurally critical nodes, resulting in accelerated network disintegration, reducing the giant component size to 0.12 after 20% node removal compared to 0.23 for degree-based attacks, and more pronounced reductions in post attack connectivity, improves the correlation with ground-truth spreading dynamics by up to 25.1% compared to baseline methods. Furthermore, the prediction model achieves these results without reliance on domain-specific priors or extensive training, balancing interpretability, computational tractability, and structural fidelity. The proposed metric offers a robust, generalizable framework for influence quantification and structural analysis in complex networked systems.

Infectious diseases pose a significant threat to global health security. Higher-order networks have recently emerged as a powerful framework to capture group-based transmission processes. Conventional studies often assume that transmission probabilities scale with group size; however, such probabilities may in fact remain constant due to intrinsic epidemiological properties. In other words, the apparent variation of transmission probabilities may instead arise from additive effects which may stem from time scale variations for various group sizes based on the existing studies. The group-size based multiscale influence on the dynamics is unclear. To elucidate this mechanism, we propose a multiscale epidemic model on hypergraphs incorporating two- and three-body interactions, where transmission intensities are used to unify heterogeneous temporal scales. Two extreme mechanisms are analyzed: individual and group transmission models. We derive the basic reproduction number R0 and perform bifurcation analysis. Our results reveal that R0 depends on both pairwise and triadic transmission intensities and yields only forward bifurcation in individual transmission, whereas in group transmission R0 depends solely on the latter but exhibits backward bifurcation. Subsequently, Monte Carlo simulations validate the models' rationality and further numerical simulations demonstrate that triadic transmission intensity markedly alters the basic reproduction number, steady states, and region distributions of the solutions. These findings highlight how additive effects of group interactions drive multiscale epidemic dynamics, offering new insights into higher-order mechanisms underlying infectious disease spread.

We investigate the recovery dynamics of healthy cardiac activity after physical exertion using multimodal biosignals recorded with a polycardiograph. Multifractal features derived from the singularity spectrum capture the scale-invariant properties of cardiovascular regulation. Five supervised classification algorithms-Logistic Regression (LogReg), Support Vector Machine with radial basis function kernel, k-Nearest Neighbors, Decision Tree, and Random Forest-were evaluated to distinguish recovery states in a small, imbalanced dataset. Our results show that multifractal analysis, combined with multimodal sensing, yields reliable features for characterizing recovery and points toward nonlinear diagnostic methods for heart conditions.

It is demonstrated that the widely used Lennard-Jones (LJ) potential in the mechanics of cross-linked polymers-and an oscillator based on it-can give rise to several notable phenomena: (i) The emergence of subharmonic and superharmonic oscillations across a broad range of driving force amplitudes; (ii) the presence of exponentially decaying amplitudes in the discrete part of the amplitude spectrum, associated with superharmonic components; (iii) the manifestation of multi-periodic, quasi-periodic, and chaotic regimes, depending on the amplitude of the driving force; (iv) the appearance of Feigenbaum cascades at transition zones between multi-periodic and chaotic behavior; and (v) the formation of strange attractors in the corresponding Poincaré sections, indicative of chaotic dynamics. The analysis is based on solving an autonomous system of three coupled first-order equations using the Adams-Bashforth-Moulton solver, which is well-suited for stiff dynamical systems. These findings offer deeper insight into the vibrational performance of seismic and vibration absorbers constructed from rubber-like materials modelled by LJ potentials.

To describe the heterogeneity of the neural network, we propose an anomalous random neural network (ARNN) with arbitrary distributed waiting times, which is a generalization of the random neural network. We investigate the signal flow process in ARNN based on the renewal process and obtain the generalized master equations for the time evolution of the probability of the state vector of neurons. From the obtained master equations, we obtain the generalized rate equations for the time evolution of the average potential of each neuron in both closed and open ARNN systems. It is proved that when the distribution of waiting time is exponential, the generalized rate equations for open ARNN systems can reduce to Hopfield neural networks; when the distribution of waiting time is power-law, the corresponding rate equations become the generalized fractional-order Hopfield neural networks. Particularly, for a single neuron, we derive a power-law firing rate that matches the experiment [Lundstrom et al., Nat. Neurosci. 11, 1335 (2008)].

The Largest Lyapunov Exponent (LLE) is a fundamental diagnostic of chaotic behavior in nonlinear dynamical systems, quantifying the exponential divergence of nearby trajectories. Classical computational approaches, such as Wolf's algorithm, track individual particle trajectories to estimate the LLE, but these techniques face challenges related to noise sensitivity, computational efficiency, and scalability to high-dimensional systems. This work introduces a novel variance-based methodology for computing the LLE using intrusive polynomial chaos (IPC), an uncertainty quantification technique that evolves the probability distribution of initial conditions under deterministic dynamics rather than tracking discrete trajectories. The key innovation is extracting the LLE from the exponential growth rate of ensemble variance, which connects deterministic chaos with probabilistic descriptions. Validation against the classical trajectory-based algorithm is performed on three benchmark chaotic systems: the three-dimensional Lorenz and Rössler attractors, and a six-dimensional system from Al-Azzawi and Al-Obeidi, demonstrating that the IPC approach achieves comparable accuracy and convergence rates while offering the distinct advantage of directly computing the full statistical structure of ensemble dynamics. Comparison of convergence histories, probability density functions of instantaneous Lyapunov exponents, and statistical error measures confirms excellent agreement between the proposed IPC-based methodology and established algorithms. The results indicate that variance-based LLE estimation via polynomial chaos is a robust and viable alternative to trajectory-based methods.

We study the formation and collision of 1D (one-dimensional) and 2D (two-dimensional) Gaussian-shaped and flat-top (FT) solitons in the framework of the nonlinear Schrödinger equation with the cubic-quintic nonlinearity and two intersecting potential troughs. We find that Gaussian-Gaussian and Gaussian-FT collisions between the solitons, steered by the troughs, are quasi-elastic, while the collisions between FT solitons may be either quasi-elastic or inelastic, in the form of merger into a single FT soliton, thus spontaneously breaking the symmetry between the steering troughs. The Gaussian-FT collisions, being overall quasi-elastic, generate weak radiation fields.

This work explores a chaotification technique that consists of the composition of exponential functions with offset boosting, in which the exponential term includes a seed function in its exponent. This architecture offers a high degree of design freedom, as several different map families can be designed, considering the number of compositions, the values of the control parameters, and the type of seed function. Based on this general family of maps, three different map examples are designed. Several analytical results are provided regarding the Lyapunov exponent expression and the existence of fixed points. The maps are then also studied numerically, through computation of cobweb, fixed point, bifurcation, and Lyapunov exponent diagrams. Interesting behaviors are observed, like the absence of fixed points and thus hidden attractors, as well as robust chaos. The maps are then successfully applied to the problem of pseudorandom bit generation. Overall, this family of maps gives very promising results for further studies.

Complex systems are commonly modeled using graphs, where nodes represent entities and edges represent pairwise interactions. Yet, many real-world systems exhibit higher-order interactions that involve multiple entities simultaneously and cannot be adequately captured by pairwise links. Simplicial complexes offer a mathematical framework for modeling such higher-order structures, where interactions among sets of nodes are represented as simplices-such as vertices (0-simplices), edges (1-simplices), and triangles (2-simplices). In practical applications, the sizes of these higher-order interactions can vary significantly. To reflect this heterogeneity, we introduce a growing simplicial complex model in which the dimensions of newly added simplices are sampled from a predefined probability distribution. Theoretical analysis reveals that the generalized degree of faces in this model follows a power-law distribution, with exponents that can be adjusted by varying the simplex-dimension distribution. Numerical simulations support these theoretical predictions and illustrate the model's capacity to generate simplicial complexes with customizable structural properties. Overall, this model offers a versatile theoretical framework for studying heterogeneous higher-order structures and their emergent properties in higher-order systems.

As a regularization of the Hadamard type fractional derivative and a natural extension of the Caputo-Hadamard fractional derivative, the Caputo-Hadamard type fractional derivative exhibits exceptional compatibility, serving as a tractable tool for precise characterization of ultra-slow varying dynamical processes. Compared with Lyapunov stability within the framework of an infinite-time horizon, achieving prescribed performance in finite-time is imperative for practical applications. Herein, this paper concentrates on the finite-time stability of Caputo-Hadamard type fractional differential systems [C-HTFDSs] under two scenarios: systems without delays and systems with proportional delays. To achieve this, for both linear (homogeneous/nonhomogeneous) and nonlinear cases without time delays, the finite-time stability criteria are established leveraging a modified Laplace transform technique and an adaptive fractional Gronwall type inequality, respectively. Then, with regard to the homogeneous and nonhomogeneous linear C-HTFDSs with proportional delays, two novel proportional delayed Mittag-Leffler matrix functions are designed separately, leading to the sound formulations of their fundamental solutions. Finally, as to the nonlinear C-HTFDS with proportional delay, a compatible proportional retarded fractional Gronwall type inequality with two integral terms is constructed and demonstrated in detail. Not only that, several indispensable numerical simulations are implemented to validate the effectiveness and practicality of the theoretical findings.