Chaos最新文献

In recent decades, researchers have used interdependent networks and interdependent higher-order networks to model real-world interdependent systems that exhibit only low-order (pairwise interactions) or higher-order relationships. However, in real life, both higher-order and low-order relationships often coexist. For example, in a Cyber-Physical System (CPS), the communication relationships between nodes in the network layer represent low-order relations, whereas the collection of devices located within the same physical area in the physical layer constitutes higher-order relations. Therefore, this paper investigates a hybrid interdependent higher-order network model that incorporates both low-order and higher-order relationships, with the latter represented by a hypergraph. By randomly removing nodes from the network, we systematically analyze the robustness of this model. A unified theoretical framework is proposed, and experiments are conducted on artificial and real-world networks with different topological structures. The experimental results show that the theoretical predictions are highly consistent with the simulation results. These findings not only deepen our understanding of the robustness of hybrid interdependent higher-order networks but also provide new theoretical insights for preventing failures in such networks.

We present the first closed-form analytical characterization of local oscillatory dynamics in the adaptive exponential integrate-and-fire (AdEx) model, a key framework for understanding neural excitability and adaptation. By combining standard rescaling with rigorously bounded polynomial approximations of the exponential nonlinearity, we derive three unprecedented analytical results: (1) explicit Hopf bifurcation loci (trace-zero conditions) and stability criteria; (2) closed-form expressions for the first Lyapunov coefficient determining bifurcation type (subcritical vs supercritical) and neural excitability class (type-I vs type-II); and (3) leading-order period coefficients (T2, T3) characterizing how oscillation frequency depends on amplitude near bifurcation. For cubic approximations, we additionally characterize transitions between monoequilibria and triequilibria regimes, with implications for multistability and working memory. We provide rigorous local validity guarantees (|v-v∗|<0.6 ensures <1% and <5% errors for cubic and quadratic approximations, respectively) and quantify Taylor remainders. These closed-form results enable direct parameter-to-behavior mappings without numerical integration. We validate predictions against the full exponential model and demonstrate practical utility through genetic-algorithm-based parameter fitting to experimental AgRP neuron recordings. This work connects analytical tractability with empirical accuracy, offering both mechanistic insights into how adaptation shapes neural oscillations and computational efficiency for fitting models to data. While inherently local by construction, these results complement existing global reduction approaches and provide explicit coefficients unavailable from previous methods, opening new avenues for understanding adaptation-dependent dynamics in spiking neural networks.

We introduce an effective algorithmic method for the computation of a lower bound for uniform expansion in one-dimensional dynamics. The approach employs interval arithmetic and thus provides a rigorous numerical result (computer-assisted proof). The method uses efficient graph algorithms and an iterative approach for optimal performance. A software implementation of the method is made publicly available. This is an example of a quantitative result in the theory of dynamical systems, as opposed to many qualitative results whose assumptions may be difficult to verify and the conclusions may have limited use in practical models that describe natural phenomena. We discuss and illustrate the effectiveness of our method and apply it to the quadratic map family.

We consider the basic tight-binding model for an array of waveguide arrays with periodic zigzag modulations in the longitudinal direction and local Kerr nonlinearity, focusing on the case with zero average modulation. From the Floquet spectrum of the linearized Su-Schrieffer-Heeger (SSH)-like system, we identify the various gaps where nonlinear solutions may exist, exponentially localized in the bulk and/or at edges. For the fully nonlinear system, numerical continuation yields families of exponentially localized Floquet lattice solitons, calculated to computer precision. Numerical Floquet linear stability analysis shows regimes of stability and explores instability scenarios appearing from internal mode resonances.

The microscopic structure of several amorphous substances often reveals complex patterns such as medium- or long-range order, spatial heterogeneity, and even local polycrystallinity. To capture all these features, models usually incorporate a refined description of the particle interaction that includes an ad hoc design of the inside of the system constituents and use temperature as a control parameter. We show that all these features can emerge from a minimal athermal two-dimensional model where particles interact isotropically by a double-well potential, which includes an excluded volume and a maximum coordination number. The rich variety of structural patterns shown by this simple geometrical model apply to a wide range of real systems including water, silicon, and different amorphous materials.

We investigate synchronization in a quantum reservoir computing (QRC) system when learning chaotic system of interest. By training a QRC model to learn the dynamical equations of chaotic systems, we confirmed its ability to capture the dynamics of nonlinear time series. Based on this, we constructed a drive-response synchronization framework consisting of two independently trained QRC models, and the response model was evaluated by analyzing the Euclidean distance between their predicted values. Additionally, we systematically study the influence of coupling strength on synchronization performance, revealing the crucial role of coupling parameters in the synchronization evolution. Moreover, this study not only demonstrated the potential of quantum reservoir computing in simulating chaotic systems but also verified the feasibility of synchronous prediction among multiple independent quantum reservoir systems under external driving by introducing a synchronization mechanism.

In this paper, we investigate the dynamics of a relativistic particle confined to a ring. The focus is on the metamorphoses of the functional form of the particle propagator induced by a change in the asymptotic parameter, proportional to the ratio of the ring length to the particle Compton wavelength. Tackling the divergent nature of the propagator enabled us to describe and classify all patterns produced by particle self-interference, regardless of the shape of the initial wave packet. We shall show under which conditions a quasiperiodic structure, known as quantum carpets, arises and demonstrate that its quartic part of the phase function, which structurally stabilizes the canonical carpet, is not just a correction but explains all features of the exact solution.

The paradigm of higher-order interactions has received considerable attention in recent years. Previous studies have reported that coupled phase oscillator systems exhibit extensive multistability and abrupt desynchronization transitions in the presence of non-pairwise interactions. This study advances current understanding by systematically comparing three distinct coupling strategies. The findings reveal that the addition of a higher (second) coupling mode and adaptive coupling enables the emergence of these complex macroscopic behaviors in systems with pairwise coupling. A theoretical framework is developed to elucidate the dynamic origins of these states. In particular, the mechanisms underlying multistability are clarified, the causes of irreversible abrupt desynchronization transitions are identified, and the critical scaling relationships between the Kuramoto and Daido order parameters and coupling strength are explored.

The study of temporal higher-order networks is crucial for forecasting phenomena such as information spread and systemic resilience. However, previous dominant models like the higher-order activity-driven framework capture connection formation but overlook the crucial role of dissolution in network dynamics. This omission biases predictions of network evolution and stability. In this article, we introduce the higher-order activity-vulnerability driven (HOAVD) networks, a novel framework that simultaneously captures hyperedge formation and dissolution by activity and vulnerability of nodes. We show that the competition between these two attributes induces a gradual dynamic phase transition at a characteristic timescale, separating the dynamics into a short-timescale, activity-dominated regime and a long-timescale, balanced regime. Meanwhile, we obtain analytical expressions of topological property of HOAVD networks. Moreover, we derive an critical balance condition for system-wide percolation in the balanced regime. This condition reveals that the connectivity is sensitively constrained by the statistical interplay between the distributions of activity and vulnerability, a phenomenon representing a fundamental mechanism that was invisible to previous models. Our analytical results, which also provide insights into the time-dependent topology, are supported by numerical simulations of real data. Therefore, the HOAVD framework offers a more complete and physically grounded foundation for predicting and controlling dynamics in social, biological, and technological systems.

There are numerous indicators used to characterize the degree of synchronization for a non-identical system consisting of heterogeneous phase oscillators, such as the critical coupling of phase synchronization and the critical coupling of frequency synchronization and order parameter. Is it possible to predict these indicators simultaneously given the realistic situations of unknown system dynamics, including network structure, local dynamics, and coupling functions? This process, known as multi-task learning, can be achieved through the model-free technique of a feed-forward neural network in machine learning. To elaborate, we can measure the synchronization indicators of a limited number of allocation schemes and utilize these data to train the machine model. Once trained, the model can be employed to predict these indicators simultaneously for any novel allocation scheme. More importantly, the trained machine can also identify the optimal allocation for synchronization from a large pool of candidates. This method solves an outstanding question, which is how to allocate a given set of heterogeneous oscillators on a complex network in order to improve the synchronization performance. Leveraging multi-task learning's ability to predict multiple synchronization indicators, we can ensure that the system with the optimal performs well throughout the entire synchronization transition. Additionally, we test the scalability of the machine; one approach is to predict the indicators for a system composed of a new set of oscillators, and the other is to simultaneously predict the indicators of different systems.