Chaos最新文献

The spread of misinformation on social media is inextricably related to each user's forwarding habits. In this paper, given that users have heterogeneous forwarding probabilities to their neighbors with varied relationships when they receive misinformation, we present a novel ignorant-spreader-refractory (ISR) spreading model with heterogeneous spreading rates on activity-driven networks with various types of links that encode these differential relationships. More exactly, in this model, the same type of links has an identical spreading rate, while different types of links have distinct ones. Using a mean-field approach and Monte Carlo simulations, we investigate how the heterogeneity of spreading rates affects the outbreak threshold and final prevalence of misinformation. It is demonstrated that the heterogeneity of spreading rates has no effect on the threshold when the type of link follows a uniform distribution. However, it has a significant impact on the threshold for non-uniform distributions. For example, the heterogeneity of spreading rates increases the threshold for normal distribution while it lowers the threshold for an exponent distribution. In comparison to the situation of a homogeneous spreading rate, whether the heterogeneity of spreading rates improves or decreases the final prevalence of misinformation is also determined by the distributions of the type of links.

This article presents an overview of an mpox epidemiological situation in the most affected regions-Africa, Americas, and Europe-tailoring fractal interpolation for pre-processing the mpox cases. This keen analysis has highlighted the irregular and fractal patterns in the trend of mpox transmission. During the current scenario of public health emergency of international concern due to an mpox outbreak, an additional significance of this article is the interpretation of mpox spread in light of multifractality. The self-similar measure, namely, the multifractal measure, is utilized to explore the heterogeneity in the mpox cases. Moreover, a bidirectional long-short term memory neural network has been employed to forecast the future mpox spread to alert the outbreak as it seems to be a silent symptom for global epidemic.

Non-stationary systems are found throughout the world, from climate patterns under the influence of variation in carbon dioxide concentration to brain dynamics driven by ascending neuromodulation. Accordingly, there is a need for methods to analyze non-stationary processes, and yet, most time-series analysis methods that are used in practice on important problems across science and industry make the simplifying assumption of stationarity. One important problem in the analysis of non-stationary systems is the problem class that we refer to as parameter inference from a non-stationary unknown process (PINUP). Given an observed time series, this involves inferring the parameters that drive non-stationarity of the time series, without requiring knowledge or inference of a mathematical model of the underlying system. Here, we review and unify a diverse literature of algorithms for PINUP. We formulate the problem and categorize the various algorithmic contributions into those based on (1) dimension reduction, (2) statistical time-series features, (3) prediction error, (4) phase-space partitioning, (5) recurrence plots, and (6) Bayesian inference. This synthesis will allow researchers to identify gaps in the literature and will enable systematic comparisons of different methods. We also demonstrate that the most common systems that existing methods are tested on-notably, the non-stationary Lorenz process and logistic map-are surprisingly easy to perform well on using simple statistical features like windowed mean and variance, undermining the practice of using good performance on these systems as evidence of algorithmic performance. We then identify more challenging problems that many existing methods perform poorly on and which can be used to drive methodological advances in the field. Our results unify disjoint scientific contributions to analyzing the non-stationary systems and suggest new directions for progress on the PINUP problem and the broader study of non-stationary phenomena.

The mixing groups gathered in the enclosed space form a complex contact network due to face-to-face interaction, which affects the status and role of different groups in social communication. The intricacies of epidemic spreading in mixing groups are intrinsically complicated. Multiple interactions and transmission add to the difficulties of understanding and forecasting the spread of infectious diseases in mixing groups. Despite the critical relevance of face-to-face interactions in real-world situations, there is a significant lack of comprehensive study addressing the unique issues of mixed groups, particularly those with complex face-to-face interactions. We introduce a novel model employing an agent-based approach to elucidate the nuances of face-to-face interactions within mixing groups. In this paper, we apply a susceptible-infected-susceptible process to mixing groups and integrate a temporal network within a specified time window to distinguish between individual movement patterns and epidemic spreading dynamics. Our findings highlight the significant impact of both the relative size of mixing groups and the groups' mixing patterns on the trajectory of disease spread within the mixing groups. When group sizes differ significantly, high inter-group contact preference limits disease spread. However, if the minority reduces their intra-group preferences while the majority maintains high inter-group contact, disease spread increases. In balanced group sizes, high intra-group contact preferences can limit transmission, but asymmetrically reducing any group's intra-group preference can lead to increased spread.

In this article, we present evidence of a distinct class of extreme events that occur during the transient chaotic state within network modeling using the Brusselator with a mutually coupled star network. We analyze the phenomenon of transient extreme events in the network by focusing on the lifetimes of chaotic states. These events are identified through the finite-time Lyapunov exponent and quantified using threshold and statistical methods, including the probability distribution function (PDF), generalized extreme value (GEV) distribution, and return period plots. We also evaluate the transitions of these extreme events by examining the average synchronization error and the system's energy function. Our findings, validated across networks of various sizes, demonstrate consistent patterns and behaviors, contributing to a deeper understanding of transient extreme events in complex networks.

In this paper, we investigate a seven-parameter, five-dimensional dynamical system, specifically a unidirectional coupling of two FitzHugh-Nagumo neuron models, with one neuron being sinusoidally driven. This master-slave configuration features neuron N1 as the master, subjected to an external sinusoidal electrical current, and neuron N2 as the slave, interacting with N1 through an electrical force. We report numerical results for three distinct scenarios where N1 operates in (i) periodic, (ii) quasiperiodic, and (iii) chaotic regimes. The primary objective is to explore how the dynamics of the master neuron N1 influence the coupled system's behavior. To achieve this, we generated cross sections of the seven-dimensional parameter space, known as parameter planes. Our findings reveal that in the periodic regime of N1, the coupled system exhibits period-adding sequences of Arnold tongue-like structures in the parameter planes. Furthermore, regions of multistability can also be identified in these parameter planes of the coupled system. In the quasiperiodic regime, regions of periodic motion are absent, with only regions of quasiperiodic and chaotic dynamics present. In the chaotic regime of N1, the parameter planes display regions of chaos, hyperchaos, and transient hyperchaos.

In this paper, we present a new method of performing extended dynamic mode decomposition (EDMD) on systems, which admit a symbolic representation. EDMD generates estimates of the Koopman operator, K, for a dynamical system by defining a dictionary of observables on the space and producing an estimate, Km, which is restricted to be invariant on the span of this dictionary. A central question for the EDMD is what should the dictionary be? We consider a class of chaotic dynamical systems with a known or estimable generating partition. For these systems, we construct an effective dictionary from indicators of the "cylinder sets," which arise in defining the "symbolic system" from the generating partition. We prove strong operator topology convergence for both the projection onto the span of our dictionary and for Km. We also prove practical finite-step estimation bounds for the projection and Km as well. Finally, we demonstrate some numerical results on eigenspectrum estimation and forecasting applied to the dyadic map and the logistic map.

Exact solution for the probability density function is considered for two coupled population growth models driven by Gaussian white noises. Moreover, n-moments of interactions of the Gompertz and Verhulst logistic models are obtained and analyzed. It is shown that interactions can modify the behaviors of the population growth models, i.e, the species may collaborate and/or compete between them.

How do complex adaptive systems, such as life, emerge from simple constituent parts? In the 1990s, Walter Fontana and Leo Buss proposed a novel modeling approach to this question, based on a formal model of computation known as the λ calculus. The model demonstrated how simple rules, embedded in a combinatorially large space of possibilities, could yield complex, dynamically stable organizations, reminiscent of biochemical reaction networks. Here, we revisit this classic model, called AlChemy, which has been understudied over the past 30 years. We reproduce the original results and study the robustness of those results using the greater computing resources available today. Our analysis reveals several unanticipated features of the system, demonstrating a surprising mix of dynamical robustness and fragility. Specifically, we find that complex, stable organizations emerge more frequently than previously expected, that these organizations are robust against collapse into trivial fixed points, but that these stable organizations cannot be easily combined into higher order entities. We also study the role played by the random generators used in the model, characterizing the initial distribution of objects produced by two random expression generators, and their consequences on the results. Finally, we provide a constructive proof that shows how an extension of the model, based on the typed λ calculus, could simulate transitions between arbitrary states in any possible chemical reaction network, thus indicating a concrete connection between AlChemy and chemical reaction networks. We conclude with a discussion of possible applications of AlChemy to self-organization in modern programming languages and quantitative approaches to the origin of life.

Link prediction has a wide range of applications in the study of complex networks, and the current research on link prediction based on single-layer networks has achieved fruitful results, while link prediction methods for multilayer networks have to be further developed. Existing research on link prediction for multilayer networks mainly focuses on multiplexed networks with homogeneous nodes and heterogeneous edges, while there are relatively few studies on general multilayer networks with heterogeneous nodes and edges. In this context, this paper proposes a method for heterogeneous multilayer networks based on motifs for link prediction. The method considers not only the effect of heterogeneity of edges on network links but also the effect of heterogeneous and homogeneous nodes on the existence of links between nodes. In addition, we use the role function of nodes to measure the contribution of nodes to form the motifs with links in different layers of the network, thus enabling the prediction of intra- and inter-layer links on heterogeneous multilayer networks. Finally, we apply the method to several empirical networks and find that our method has better link prediction performance than several other link prediction methods on multilayer networks.