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• The citations of 729,515 articles fit by the generalized extreme-value distribution. • The complexity of references and citations of papers' quantiles is studied. • The macroscopic model of the citation distribution is proposed. The paper presents an in-depth study of uncited papers. For that, we explore the documents indexed in the INSPIRE database from 1970 to 2015. Uncited articles represent a complex bibliometric environment in which references are generated. The reference lists of uncited papers form a dynamic system partially responsible for the redistribution of scientific impact. Our task is to quantify the detailed structure of citations and references directly in terms of quantiles. We also study the entropy and the statistical complexity measure of references and citations of papers' quantiles. We introduce a theoretical framework in which citation distribution is considered an asymptotic distribution of the largest values in a sequence of independent identically distributed random variables. We show that this asymptotic distribution is the generalized extreme-value distribution. Furthermore, we empirically demonstrate that the asymptotic behavior of citation distribution is close to (but not quite) the generalized extreme-value distribution. [ABSTRACT FROM AUTHOR]

This paper is concerned with the design of positive L1$$ {L}_1 $$ filter for positive Markovian jump systems (PMJSs) with adaptive event‐triggered mechanism and quantization. Considering the mode jump of the system, a new adaptive event‐triggered condition is established, which not only can regulate the communication threshold according to the error of dynamic systems, but also can avoid the asynchronous phenomenon between the system mode and the filter mode. In order to further reduce the burden of communication, a new positive L1$$ {L}_1 $$ filter with the quantized measure system output is developed, and the design condition which ensures the filter error system to be stochastically stable with L1$$ {L}_1 $$ performance is presented which can be solved in terms of linear programming (LP) technique. It is illustrated that there is no Zeno phenomenon. The proposed results are applied to the power allocation in a mobile telecommunication system, and it is shown that compared with the existing results, the event‐triggered filter of this paper has some advantages. [ABSTRACT FROM AUTHOR]

Many complex physical systems exhibit a rich variety of discrete behavioural modes. Often, the system complexity limits the applicability of standard modelling tools. Hence, understanding the underlying physics of different behaviours and distinguishing between them is challenging. Although traditional machine learning techniques could predict and classify behaviour well, typically they do not provide any meaningful insight into the underlying physics of the system. In this paper we present a novel method for extracting physically meaningful clusters of discrete behaviour from limited experimental observations. This method obtains a set of physically plausible functions that both facilitate behavioural clustering and aid in system understanding. We demonstrate the approach on the V-shaped falling paper system, a new falling paper type system that exhibits four distinct behavioural modes depending on a few morphological parameters. Using just 49 experimental observations, the method discovered a set of candidate functions that distinguish behaviours with an error of 2.04%, while also aiding insight into the physical phenomena driving each behaviour. [ABSTRACT FROM AUTHOR]

Abstract: Five ratios R H , R T , S H , S T and S Z derived from the three-part division of a set of sources in h-core, h-tail and uncited sources are defined. Dynamic changes in the three independent ratios R H , S H and S Z are studied for six selected topics. Data about these topics are obtained from the Web of Science for scientific papers and Derwent Innovations Index for technical patents. It is observed that all R H - and S H -values decrease when the time span widens, while S Z stays the same or increases; and that all R H - and S H -values for papers are larger than the corresponding values for patents. The shifted Lotka distribution is used in a theoretical interpretation of these empirical phenomena. [Copyright &y& Elsevier]

In automata networks, it is well known that the way entities update their states over time has a major impact on their dynamics. In particular, depending on the chosen update schedule, the underlying dynamical systems may exhibit more or less asymptotic dynamical behaviours such as fixed points or limit cycles. Since such mathematical models have been used in the framework of biological networks modelling, the question of choosing appropriate update schedules has arised soon. In this note, focusing on Boolean networks, our aim is to emphasise that the adequate way of thinking regulations and genetic expression over time is certainly not to consider a wall segregating synchronicity from asynchronicity because they actually complement rather well. In particular, we highlight that specific update schedules, namely block-parallel update schedules, whose intrinsic features are still not known from a theoretical point of view, admit realistic and pertinent properties in the context of biological modelling and deserve certainly more attention from the community. [ABSTRACT FROM AUTHOR]

The design of a high-volume printer for professional use is rather complex. The design of the paper path and the timing of sheets is frequently reengineered as the design of the printer components progresses. This paper presents an optimization model for the combined paper path and timing design problem. The paper path is an optimal physical dimensioning problem, while the timing is an open-loop optimal control problem. The coupled optimization problem is formulated as a simultaneous analysis and design (SAND) problem using a direct transcription of the optimal control problem. Benefits of the chosen formulation for industrial application are the ease of setting up the optimization model for arbitrary printer configurations, and the short computation times. Results of an industrial case are presented. [ABSTRACT FROM AUTHOR]

In this work is presented and described an optical system specifically designed and implemented to be applied for the study of the ink–paper interaction at the paper surface, considering the two main directions of the paper sheet (machine and cross directions). This work is particularly concerned with the system description, complete characterization, test, and its usage under real conditions. Concerning the system characterization, the main parameters were addressed and set having in mind its optimization. Relatively to the test of the system, several measurements using specific object samples with known dimensions were carried out to evaluate the accuracy of the obtained results. In terms of its usage under real conditions, an experiment was carried out using a commercial ink and common copy paper to dynamically collect data of its interaction. The collected data, after processing, enabled the determination of the main results of the analyzed ink–paper interaction, which allowed to reach the following conclusions; (1) the implemented system offers two different analysis approaches (qualitative and quantitative), both showing to be in agreement; and (2) the system also shows to be important to identify variations of the ink–paper interaction, manifested in the machine and cross directions of the paper. [ABSTRACT FROM AUTHOR]

Identification of the mechanisms which permit ecological communities to maintain high levels of biodiversity is of both theoretical interest and practical importance. Intransitive competition, in which there is no single superior competitor, is known to play an important role in this problem. In this study, we undertake a systematic comparative analysis of how different competition modes and ranges affect community stability in paper–rock–scissors games. We confirm that short-ranged interactions, in combination with cyclic competition, permits relatively stable coexistence. However, in contrast to previous studies, we show that long-range interactions can also produce stable communities. This stability emerges when competition interactions create asymmetries in the opportunities for population growth depending on the abundance of the species. Our findings demonstrate that small differences in the way species compete can qualitatively change dynamic behaviours of the system, and therefore emphasize the importance of correctly identifying these competition modes when designing conservation actions. • We compare system stability among four interaction modes in cyclic competition. • We find that long-ranged competition can also produce stable coexistence. • Small differences in interaction modes qualitatively change dynamic behaviours. • We emphasize the importance of correctly identifying species competition modes. [ABSTRACT FROM AUTHOR]

In this paper, a novel repetitive control scheme is presented and discussed, based on the so-called B-spline filters. These dynamic filters are able to generate a B-spline trajectory if they are fed with the sequence of control points defining the curve. Therefore, they are ideal tools for generating online reference signals with the prescribed level of smoothness for driving dynamic systems, possibly together with a feedforward compensator. In particular, a continuous zero phase error tracking controller (ZPETC) can be used for tracking control of nonminimum phase systems but because of its open-loop nature it cannot guarantee the robustness with respect to modeling errors and exogenous disturbances. For this reason, ZPETC and trajectory generator have been embedded in a repetitive control scheme that allows to nullify interpolation errors even in nonideal conditions, provided that the desired reference trajectory and the disturbances are periodic. This paper is based on the results presented in the conference paper [L. Biagiotti, F. Califano, and C. Melchiorri, “Repetitive control of non-minimum phase systems along b-spline trajectories,” in Proc. IEEE 55th Conf. Decis. Control, 2016, pp. 5496–5501.], where asymptotic stability of the overall control scheme has been proved mathematically, but extends such results with an experimental validation based on a nonminimum phase system. Different models of the same physical system have been identified and used in the implementation of this model-based control scheme, allowing a real evaluation of the relationship between control system performance and model accuracy. [ABSTRACT FROM AUTHOR]

This paper presents a detailed model of low-frequency oscillations and their damping within the Electric Power System (EPS) of Bosnia and Herzegovina (B&H). The system is modeled using MATLAB software, analysing the steady state and dynamic responses. This research highlights the challenges and impacts of integrating renewable energy sources, such as wind farms, on grid stability and oscillation damping. The paper utilizes eigenvalue analysis to investigate the dynamic characteristics of the system, emphasizing the need for efficient damping strategies to maintain system stability. The methodology includes a comprehensive review of existing literature, the creation of a detailed EPS model of B&H, and the application of eigenvalue and oscillation amplitude analysis to determine damping ratios. The dynamic responses of hydro power plants, HPP Mostar and HPP Jablanica, to transient disturbances are analysed to validate the model and refine damping strategies. The results indicate that the B&H EPS is well-damped, with all eigenvalues possessing negative real parts, and demonstrate the system's resilience to small disturbances. The results are compared with the technical report on the integration of the wind power plant WPP Podveležje. This comparative analysis shows consistent patterns between the modeled calculations and empirical data, confirming the robustness of the EPS model. This alignment underscores the effectiveness of current damping mechanisms and provides a foundational strategy for enhancing system stability with increasing renewable energy penetration. The findings highlight the importance of developing advanced control strategies to sustain system stability as the integration of variable renewable energy sources continues to grow. [ABSTRACT FROM AUTHOR]

This Special Issue of Applied Mathematical Modelling journal consists of selected quality papers originally presented at 15th International Conference "Dynamical Systems - Theory and Applications" (DSTA) which took place on December 2-5, 2019 in Lodz, Poland. B Dzyubak et al. b analysed a non-linear multi-scale diffusion cancer invasion model that describes the interactions of the tumour cells, matrix-metalloproteinases, matrix-degradative enzymes and oxygen. Chaotic cancer attractors are quantified and multi-parametric evolution of conditions leading to cancer invasion is defined. [Extracted from the article]

In a circular economy, extended producer responsibility (EPR) is a regulatory approach that accounts for all environmental costs associated with a product throughout its life cycle. When considering the EPR, the regulator must (1) design an integrated framework for different stakeholders and (2) provide effective policies to create financial incentives to accelerate the circular system. Recycling funds and subsidies are the most prominent financial strategies that can either encourage or curtail the flows of recycled products. In Indonesia, a few companies provided recycling bonus s to their customers as incentives to increase the recycling rate. However, the recycling rate was not as effective as expected by the enterprise because recycling was practiced by a limited number of companies, rendering it economically unviable. The enterprises hope the government could develop a recycling fund system. In order to develop the recycling fund system, a system dynamic model was proposed and simulated to optimize the recycling funds and subsidies based on decentralized reverse supply chains. Although it is not a novelty model; however, the research show a very significant results for the government in Indonesia. This enabled a more precise, well-planned, and sustainable decision-making process for the EPR. In addition, by utilizing the system dynamic model with different scenarios in a real case study (aseptic paper packaging waste), we found that the capacity of the recycler could become the reference for the funds to be paid by the importer-producer group, wherein the recycling rate will increase with an increase in the recycling fund. • When formulating an EPR scheme, two points must be considered: framework and policies. • A system dynamic model was proposed and simulated to get the optimal solution. • A related case study involving aseptic paper packaging (APP) was considered. [ABSTRACT FROM AUTHOR]

Current research on SLAM can be divided into two parts according to the research scenario: SLAM research in dynamic scenarios and SLAM research in static scenarios. Research is now relatively well established for static environments. However, in dynamic environments, the impact of moving objects leads to inaccurate positioning accuracy and poor robustness of SLAM systems. To address the shortcomings of SLAM systems in dynamic environments, this paper develops a series of solutions to address these problems. First, an attention-based Mask R-CNN network is used to ensure the reliability of dynamic object extraction in dynamic environments. Dynamic feature points are then rejected based on the mask identified by the Mask R-CNN network, and a preliminary estimate of the camera pose is made. Secondly, in order to enhance the picture matching quality and efficiently reject the mismatched points, this paper proposes an image mismatching algorithm incorporating adaptive edge distance with grid motion statistics. Finally, static feature points on dynamic objects are re-added using motion constraints and chi-square tests, and the camera's pose is re-estimated. The SLAM algorithm of this paper was run on the KITTI and TUM-RGBD datasets, respectively, and the results show that the SLAM algorithm of this paper outperforms the ORB-SLAM2 algorithm for sequences containing more dynamic objects in the KITTI dataset. On the TUM-RGBD dataset, the Dyna-SLAM algorithm increased localization accuracy by an average of 71.94% when compared to the ORB-SLAM2 method, while the SLAM algorithm in this study increased localization accuracy by an average of 78.18% when compared to the ORB-SLAM2 algorithm. When compared to the Dyna-SLAM technique, the SLAM algorithm in this work increased average positioning accuracy by 6.24%, proving that it is superior to Dyna-SLAM. [ABSTRACT FROM AUTHOR]

Hardware-in-the-loop (HIL) testing is a popular control system testing method because it bridges the gap between modeling/simulation and experiments. Instead of designing a full hardware-based experiment to validate the results of a simulation, the plant hardware can be replaced with an emulator device that responds to exogenous inputs and effectively emulates the dynamic behavior of a system. This approach can be more cost-effective and modular, since the emulated plant system can be modeled in a simulation environment, implemented on a simplified piece of hardware and changed quickly without having to fabricate new parts. This paper develops the hardware and control scheme for a certain type of HIL device called a dynamic load emulator that consists of a 1-DOF linear hydraulic dynamometer equipped with in-line sensing to measure both its own position and the force exerted on it by a device-under-test. This measured force is passed to a real-time model of the emulated dynamic system. The model outputs the emulated system position, and a closed-loop controller is used to emulate this position. The emulator controller incorporates both model-based feedforward and standard feedback PI control. This paper characterizes the dynamometer-based dynamic load emulator and its controller, determining its hardware limitations and validating its capabilities when experiencing a force input from a linear spring with known parameters. Additionally, this paper demonstrates the ability of the emulator to represent the dynamics of a 1-DOF robotic joint when actuated by a pair of fluidic artificial muscles (FAMs). The primary contribution of this work is to allow for more comprehensive testing of FAM configurations, topologies, and controllers for a wide range of parameters, because the same hardware can be used to emulate multiple systems. As a result, this work will lead to more cost-effective, time-efficient, and energy-efficient designs of robotic systems and the FAMs used to actuate them. [ABSTRACT FROM AUTHOR]

This is a complementation work of the paper referred in Jorge Silva, Muñoz Rivera and Racke (Appl Math Optim 73:165–194, 2016) where the authors proposed a semi-linear viscoelastic Kirchhoff plate model. While in [28] it is presented a study on well-posedness and energy decay rates in a historyless memory context, here our main goal is to consider the problem in a past history framework and then analyze its long-time behavior through the corresponding autonomous dynamical system. More specifically, our results are concerned with the existence of finite dimensional attractors as well as their intrinsic properties from the dynamical systems viewpoint. In addition, we also present a physical justification of the model under consideration. Hence, our new achievements complement those established in [28] to the case of memory in a history space setting and extend the results in Jorge Silva and Ma (IMA J Appl Math 78:1130–1146, 2013, J Math Phys 54:021505, 2013) to the case of dissipation only given by the memory term. [ABSTRACT FROM AUTHOR]

Runtime verification (RV) refers to methods for formal reasoning about all aspects of the dynamic execution of systems, including hardware, software, and cyber-physical systems. RV includes techniques to assess and enforce correctness of a system against systemic bugs or extrinsic uncertainties. These methods are typically considered lightweight as they may not involve exhaustive verification or proofs, but they provide a higher level of rigor and versatility compared to conventional testing methods. This article introduces the extended versions of selected papers from the peer-reviewed proceedings of the 20th International Conference on Runtime Verification (RV 2020). RV 2020 was supposed to be held in Los Angeles, California, USA in July 2020, but was instead held virtually due to the global Covid-19 pandemic. [ABSTRACT FROM AUTHOR]

In this paper, the qualitative behaviors of an important four-dimensional Lorenz system with wild pseudohyperbolic attractor that proposed in (Gonchenko et al 2021 Nonlinearity 34 2018–47) are considered. Here, we prove that the four-dimensional Lorenz system with varying parameters is global bounded according to Lyapunov's direct method. Furthermore, we provide a collection of global absorbing sets, where in addition we obtain the rate of the trajectories going from the exterior to the global absorbing set. In particular, we solve the critical case k → 0 + that cannot be resolved by using the previous methods. The fundamental qualitative behaviors are analyzed theoretically and numerically. We present bifurcation diagrams to further explore the complicated dynamical behaviors of this system. The period-doubling bifurcation phenomenon is found. To illustrate the efficiency of our method, we present numerical simulations to show the validity of our research results. Finally, we present some applications of our research results in this paper. [ABSTRACT FROM AUTHOR]

This paper presents the Load Frequency Control of two modern interconnected power systems. Area 1 comprises a combination of conventional generators, Solar PV, and Solar Thermal, while Area 2 combines conventional generators with wind and Solar Thermal. Governor dead band and appropriate generation rate constraints are considered for conventional generators in both areas. Additionally, Superconducting Magnetic Energy Storage (SMES) and Battery Energy Storage (BES) are the two forms of energy storage units (ES) included in the system. The three controllers PID, TiltIntegral-Derivative (TID), and Fractional-Order Proportional-Integral-Derivative (FOPID) are investigated and compared for TAMSPS. The controller gains are optimized using the PSO algorithm. The system dynamic performances are studied with a 1% step load perturbation and random loads in Area 1 with different controllers. [ABSTRACT FROM AUTHOR]

This paper combines work to use a decision support tool for sustainable economic development, while acknowledging interdependent dynamics of population density, and interferences from outside. We get new insights derived from experimental approaches: analytical models (optimal dynamic control of predator–prey models) provide optimal dynamic strategies and interventions, depending on different objective functions. Our economic experiments are able to test the applicability of these strategies, and in how far decision-makers can learn to improve decision-making by repeated applications. We aim to analyse a sustainable environment with diametrical goals to harvest as much as possible while allowing optimal population growth. We find interesting insights from those who manage the dynamic system. With the methodology of experimental economics, the experiment at hand is developed to analyse the capability of individual persons to handle a complex system, and to find an economic, stable equilibrium in a neutral setting. We have developed a most interesting simulation model, where it will turn out that prices play a less important role than availability of the goods. This aspect could become a new important aspect in economics in general and in sustainable environments especially. [ABSTRACT FROM AUTHOR]

UML diagrams are a base for the planning of development in most software projects. It is used for representing different artefacts during software development and project structure. The use case is one of the diagrams in Unified Modelling Language (UML), which allows describing the dynamic flow of the system. There are a lot of tools that are used for creating this diagram before starting the actual coding process, and the diagram needs to be specific and easily understandable. Meantime, the creation of a UML use case diagram from scratch for complex systems can be time-consuming and confusing for people, which needs to be optimised. The authors of the paper attempt to solve the addressed problem. Therefore, in this research paper a new definition for UML use case diagrams will be introduced, where the main question will be whether it is possible to formalise use case modelling by introducing pre-defined use case patterns. This is academic research and discussion, which is based on the analysis of advanced UML tools, which use case diagram templates contain. The solution to this research question contains an initial set of UML use case patterns, created by analysing of the existing use case diagram templates. Moreover, in order to validate work, the pre-defined patterns were demonstrated on a developed prototype. The operation principle of the prototype focused on giving the ability to the user to construct a use case diagram by the combination of pre-defined patterns. The prototype can be useful for the development/management process in case of correct implementation. It will allow decreasing spent time on the use case diagram creation as well as avoid creating anti-patterns. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the asymptotic stability of the trajectories governed by some delay differential inequalities on time scales. Based on time scale theory and the fixed-point theorem, some sufficient conditions are obtained for guaranteeing asymptotic stability. It is interesting that the inequalities studied in this paper include the generalized Halanay inequalities. Due to the fact that dynamic systems on a time scale unify discrete and continuous systems, the results of this paper have wider application value. Furthermore, some numerical examples verify the main results. [ABSTRACT FROM AUTHOR]

Commutation failure is still one of the most common faults in LCC-UHVDC (line commutated converter-based, ultra-high voltage direct current) systems, and if the inverter side, extinction angle, and rectification value remain constant during the fault, it may lead to commutation failure or even continuous commutation failure. Therefore, this paper first analyzes the structure of the LCC-UHVDC system and the mechanism of commutation failure and, on this basis, proposes a commutation failure suppression method based on dynamic tracking of the extinction angle rectification value. The desired DC voltage of the system under fault conditions is calculated based on key state quantities such as the AC voltage RMS value, the extinction angle, and the leading angle during the fault process. The compensation amount is obtained by comparing the desired DC voltage with the actual DC voltage and superimposition on the extinction angle rectification value in the inverter extinction angle control. When there is a risk of commutation failure, dynamically adjusting the extinction angle setting value according to the compensation value is beneficial for the rapid and stable recovery of the extinction angle, reducing the probability of commutation failure. A bipolar neutral ground LCC-UHVDC testing model system is established in PSCAD/EMTDC for simulation verification to show that the proposed improved control strategy effectively reduces the probability of commutation failure and significantly improves the stable operation characteristics of the LCC-UHVDC system. [ABSTRACT FROM AUTHOR]

The subject system of this paper is of no particular interest or importance. Rather the intent is to illustrate how artificial intelligence (AI) might someday find new dynamical systems with special properties, analyze their behavior, and prepare a publication reporting the results. In fact, this entire paper was written automatically without human intervention using a template and computer program developed by the author. [ABSTRACT FROM AUTHOR]

Simultaneous Localization and Mapping (SLAM) is one of the research hotspots in the field of robotics, and it is also a prerequisite for autonomous robot navigation. The localization accuracy and stability of traditional SLAM based on static scene assumption declines due to the interference of dynamic objects. To solve the problem, this paper proposes a semantic SLAM system for dynamic environments based on object detection named DO-SLAM. Firstly, DO-SLAM uses YOLOv5 to identify objects in dynamic environments and obtains the semantic information; Then, combined with the outlier detection mechanism proposed in this paper, the dynamic objects are effectively determined and the feature points on the dynamic objects are eliminated; The combination method can reduce the interference of dynamic objects to SLAM, and improve the stability and localization accuracy of the system. At the same time, a static dense point cloud map is constructed for high-level tasks. Finally, the effectiveness of DO-SLAM is verified on the TUM RGB-D dataset. The results show that the Absolute Trajectory Error (ATE) and Relative Pose Error (RPE) are reduced, indicating that DO-SLAM can reduce the interference of dynamic objects. [ABSTRACT FROM AUTHOR]

In this paper periodic trajectories of dynamical systems presenting discontinuities are studied. The considered model consists of two distinct linear differential systems, each one containing a single equilibrium point of centre type. Each system is defined on disjoint regions of the plane, the separation line is a union of two half-straight lines contained on the coordinate axes. The obtained differential system is non-smooth, so we apply Filippov's theory to study the transitions from one dynamical system to another. The combination of the two linear plus the Filippov system acting on the separation line generates a nonlinear regime observed by the presence of limit cycles, sliding and tangential periodic trajectories as well as the coexistence of such objects. In theorem we establish the location, stability and hyperbolicity of limit cycles for certain classes of the considered model. In theorem we perform the global analysis of a representative model through bifurcation theory to analyse the birth of limit cycles, sliding periodic trajectories and tangential ones. We also provide some results addressing the coexistence of periodic trajectories and two potential physical interpretations of the model considered in the paper, one addressing nonlinear oscillations and the other considering slow-fast systems of neuron models. The main techniques employed to obtain the results are first integrals, Poincaré half return maps, and elements of bifurcation theory. [ABSTRACT FROM AUTHOR]

Timely evaluation and reperfusion have improved the myocardial salvage and the subsequent recovery rate of the patients hospitalized with acute myocardial infarction (MI). Long waiting time and time-consuming procedures of in-hospital diagnostic testing severely affect the timeliness. We present a Poincare pattern ensemble-based method with the consideration of multi-correlated non-stationary stochastic system dynamics to localize the infarct-related artery (IRA) in acute MI by fully harnessing information from paper-based Electrocardiogram (ECG). The vectorcardiogram (VCG) diagnostic features extracted from only 2.5-s long paper ECG recordings were used to hierarchically localize the IRA—not mere localization of the infarcted cardiac tissues—in acute MI. Paper ECG records and angiograms of 106 acute MI patients collected at the Heart Artery and Vein Center at Fresno California and the 12-lead ECG signals from the Physionet PTB online database were employed to validate the proposed approach. We reported the overall accuracies of 97.41% for healthy control (HC) vs. MI, 89.41 ± 9.89 for left and right culprit arteries vs. others, 88.2 ± 11.6 for left main arteries vs. right-coronary-ascending (RCA) and 93.67 ± 4.89 for left-anterior-descending (LAD) vs. left-circumflex (LCX). The IRA localization from paper ECG can be used to timely triage the patients with acute coronary syndromes to the percutaneous coronary intervention facilities. [ABSTRACT FROM AUTHOR]

The Hawkins-Simon conditions, which are necessary and sufficient for the viability of input–output systems, are described in many encyclopedias, textbooks and papers, but always without historical details about the philosopher David Hawkins. The rich literature on the history of input–output economics has neglected Hawkins, probably because he spent only a few years among the economists. My paper fills this gap. By using the relevant archival material on Hawkins, Simon, and Leontief, I correct and expand some scarce remarks on Hawkins by Simon and Samuelson. I discuss Hawkins's three remarkable contributions to economics. First, Hawkins's dynamic input–output model in Econometrica in 1948 scooped Leontief. Second, I show how the correspondence between Hawkins and Simon created their famous joint note in Econometrica in 1949. Third, an overlooked chapter in Hawkins's 1964 book The Language of Nature discussed the commodity values of commodities, generalizing Marx's labour values and the Technocrats's energy values. [ABSTRACT FROM AUTHOR]

This paper considers a model for population dynamics with age structure. Following Dufresne (2006) and Beghriche et all (2022) the probability of survival is assumed to be a linear combination of exponentials, and a product of a polynomial and an exponential. The number of births in unit time is characterized through a system of ordinary differential equations. This is solved explicitly in special cases, which leads to closed form expressions for the population size. The later allows an assymptotic analysis with three cases; the population goes extinct, explodes, or converges to a finite number depending of the interplay between model parameters. From a practical standpoint our modelling approach leads to a better fit of population data when compared to the exponential survival, and it also allows for more shapes of population as a function of time. [ABSTRACT FROM AUTHOR]

The quality of images captured digitally or transmitted over networks is distorted by noise during the process. The current methods of image restoration can be ineffective in dealing with intricate noise patterns or may be slow or imprecise. This paper fills this gap by presenting a new second-order continuous-time dynamical system for denoising of images in image restoration. The approach used in this work poses the problem as a convex quadratic program that can, thus, be solved for optimality. The existence and uniqueness of a global solution are theoretically demonstrated, and the condition for the global strong convergence of the system's trajectory is provided. The method presented in this paper is shown to be useful in a number of experiments on image restoration. As for the performance, it is higher than that of other known algorithms, with an average SNR equal to 34.78 and a Structural Similarity Index Measure (SSIM) of 0.959 for the reconstructed images. Such improvements demonstrate the effectiveness of the second-order dynamical system approach in actual image restoration applications. [ABSTRACT FROM AUTHOR]

Learning linear and nonlinear dynamical systems from available data is a timely topic in scientific machine learning. Learning must be performed while enforcing the numerical stability of the learned model, the existing knowledge within an informed or augmented setting, or by taking into account the multiscale dynamics—for both linear and nonlinear dynamics. However, when the final objective of such a learned dynamical system is to be used for control purposes, learning transformed dynamics can be advantageous. Therefore, many alternatives exists, and the present paper focuses on two of them: the first based on the discovery and use of the so-called flat control and the second one based on the use of the Koopman theory. The main contributions when addressing the first is the discovery of the flat output transformation by using an original neural framework. Moreover, when using the Koopman theory, this paper proposes an original procedure for learning parametric dynamics in the latent space, which is of particular interest in control-based engineering applications. [ABSTRACT FROM AUTHOR]

The continuous Hopfield network (CHN) is a common recurrent neural network. The CHN tool can be used to solve a number of ranking and optimization problems, where the equilibrium states of the ordinary differential equation (ODE) related to the CHN give the solution to any given problem. Because of the non-local characteristic of the "infinite memory" effect, fractional-order (FO) systems have been proved to describe more accurately the behavior of real dynamical systems, compared to the model's ODE. In this paper, a fractional-order variant of a Hopfield neural network is introduced to solve a Quadratic Knap Sac Problem (QKSP), namely the fractional CHN (FRAC-CHN). Firstly, the system is integrated with the quadratic method for fractional-order equations whose trajectories have shown erratic paths and jumps to other basin attractions. To avoid these drawbacks, a new algorithm for obtaining an equilibrium point for a CHN is introduced in this paper, namely the optimal fractional CHN (OPT-FRAC-CHN). This is a variable time-step method that converges to a good local minima in just a few iterations. Compared with the non-variable time-stepping CHN method, the optimal time-stepping CHN method (OPT-CHN) and the FRAC-CHN method, the OPT-FRAC-CHN method, produce the best local minima for random CHN instances and for the optimal feeding problem. [ABSTRACT FROM AUTHOR]

Multifactor uncertain differential equations are powerful tools for studying dynamic systems under multi-source noise. A key challenge in this study is how to accurately estimate unknown parameters based on the framework of uncertainty theory in multi-source noise environments. To address this core problem, this paper innovatively proposes a least-squares estimation method. The essence of this method lies in constructing statistical invariants with a symmetric uncertainty distribution based on observational data and determining specific parameters by minimizing the distance between the population distribution and the empirical distribution of the statistical invariant. Additionally, two numerical examples are provided to help readers better understand the practical operation and effectiveness of this method. In addition, we also provide a case study of JD.com's stock prices to illustrate the advantages of the method proposed in this paper, which not only provides a new idea and method for addressing the problem of dynamic system parameter estimation but also provides a new perspective and tool for research and application in related fields. [ABSTRACT FROM AUTHOR]

Time series forecasting has played an important role in different industries, including economics, energy, weather, and healthcare. RNN-based methods have shown promising potential due to their strong ability to model the interaction of time and variables. However, they are prone to gradient issues like gradient explosion and vanishing gradients. And the prediction accuracy is not high. To address the above issues, this paper proposes a Fractional-order Lipschitz Recurrent Neural Network with a Frequency-domain Gated Attention mechanism (FLRNN-FGA). There are three major components: the Fractional-order Lipschitz Recurrent Neural Network (FLRNN), frequency module, and gated attention mechanism. In the FLRNN, fractional-order integration is employed to describe the dynamic systems accurately. It can capture long-term dependencies and improve prediction accuracy. Lipschitz weight matrices are applied to alleviate the gradient issues. In the frequency module, temporal data are transformed into the frequency domain by Fourier transform. Frequency domain processing can reduce the computational complexity of the model. In the gated attention mechanism, the gated structure can regulate attention information transmission to reduce the number of model parameters. Extensive experimental results on five real-world benchmark datasets demonstrate the effectiveness of FLRNN-FGA compared with the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

SLAM (Simultaneous Localization and Mapping), as one of the basic functions of mobile robots, has become a hot topic in the field of robotics this year. The majority of SLAM systems in use today, however, disregard the impact of dynamic objects on the system by defining the external environment as static. A SLAM system suitable for dynamic scenes is proposed, aiming at the issue that dynamic objects in real scenes can affect the localization accuracy and map effect of traditional visual SLAM systems. Initially, the enhanced lightweight YOLOv5s target detection algorithm is employed to detect dynamic objects in each frame of the image. Simultaneously, an assessment is conducted on the feature points present on dynamic objects to determine their potential impact on system accuracy, subsequently guiding the decision to retain or exclude these feature points. The preserved static feature points are then utilized for pose estimation and map construction. Experiments on the publicly available TUM dataset and the KITTI dataset are conducted to compare the system in this paper with ORB-SLAM 3, DS-SLAM, and DynaSLAM, and the algorithm is verified to have better performance. [ABSTRACT FROM AUTHOR]

Reduced order modelling relies on representing complex dynamical systems using simplified modes, which can be achieved through the Koopman operator(KO) analysis. However, computing Koopman eigenpairs for high-dimensional observable data can be inefficient. This paper proposes using deep autoencoders(AE), a type of deep learning technique, to perform nonlinear geometric transformations on raw data before computing Koopman eigenvectors. The encoded data produced by the deep AE is diffeomorphic to a manifold of the dynamical system and has a significantly lower dimension than the raw data. To handle high-dimensional time series data, Takens' time delay embedding is presented as a preprocessing technique. The paper concludes by presenting examples of these techniques in action. [ABSTRACT FROM AUTHOR]

The evolution of universal systems has been of great interest to computer scientists. In particular, the role of Turing machines in the study of computational universality is widely recognized. Even though the patterns emerging from the evolution of this kind of dynamical system have been studied in much detail, the transition functions themselves have received less attention. In the present paper, the iota-delta function is used to encode the transition function of one-head Turing machines. In order to illustrate the methodology, we describe the transition functions of two universal Turing machines in terms of the latter function. By using the iota-delta function in this setting, Turing machines can be represented as a system of transition functions. This new representation allows us to write the transition functions as a linear combination of evolution variables wrapped by the iota-delta function. Thus, the nonlinear part of the evolution is totally described by the iota-delta function. [ABSTRACT FROM AUTHOR]

This paper studies an improved super-twisting sliding mode controller (IST-SMC) for the permanent magnet synchronous generator (PMSG) voltage loop to improve the anti-disturbance capability of the system. Compared to conventional voltage controllers, the control algorithm provides advantages in terms of system resistance to load disturbances. Conventional voltage controllers have significant voltage fluctuations and long recovery times during sudden load changes. To solve this problem, a voltage loop controller based on a super-twisting sliding mode (ST-SMC) is designed to enhance the immunity of the system. Also, the ST-SMC was improved to further increase the convergence rate of the system and enhance the dynamic performance. The convergence of the system away from the balance point is accelerated by introducing an exponential term, which in turn provides an improvement in the dynamic performance of the system. The effectiveness of the proposed control scheme was verified on a PMSG. [ABSTRACT FROM AUTHOR]

The paper is devoted to a review of recent achievements in the field of dynamic analysis of structures and structural elements, such as beams and plates, with embedded viscoelastic (VE) dampers and/or layers. The general characteristics of VE materials, their rheological models, and methods of parameters identification are discussed. New formulations of dynamic problems for systems with VE elements are also reviewed. The methods of determination of dynamic characteristics, together with the methods of analysis of steady-state and transient vibrations of such systems, are also discussed. Both linear and geometrically non-linear vibrations are considered. The paper ends with a review of the methods of sensitivity and uncertainty analysis, and the methods of optimization, for structures with VE elements. [ABSTRACT FROM AUTHOR]

Food waste is one of the most unusual behaviours related to economic systems located on the agrifood chain. In this matter, the study of the food waste and the mechanisms that lead to its development are complex and rooted within several components of the human behaviour and economic system dynamic. In this paper, we propose the development of a model which presents the dynamics of the phenomenon based on several cause-effect relationships between aspects of human behaviour and economic aspects. The model is built using a Systems Dynamic (SD) approach, based on the identification of connections between identified causes and effects and the determination of the ontologic and mathematical nature of the connections. [ABSTRACT FROM AUTHOR]

One technique, especially in chaos-based cryptographic applications, is to include the message in the evolution of the dynamical system. This paper aims to find out if and to what extent the statistical behavior of the chaotic system is affected by the message inclusion in its dynamic evolution. The study is illustrated by the dynamical system described by the logistic map in cryptographic applications based on images. The evaluation of the statistical behavior was performed on an original scheme proposed. The Monte Carlo analysis of the applied Kolmogorov–Smirnov statistical test revealed that the dynamical system in the processing scheme with message inclusion does not modify its proper statistical behavior (revealed by definition relation). This was possible due to the proposed scheme designed. Namely, this scheme contains a decision switch which, supported by an appropriate choice of the magnitude of the scaling factor, ensures that the values of the dynamical system are maintained in the definition domain. The proposed framework for analyzing the statistical properties and for preserving the dynamical system behavior is one main contribution of this research. The message inclusion scheme also provides an enhancement with cryptographic mixing functions applied internally; the statistical behavior of the dynamical system is also analyzed in this case. Thus, the paper contributes to the theoretical complex characterization of the dynamical system considering also the message inclusion case. [ABSTRACT FROM AUTHOR]

In this paper, we study large classes of nonlinear systems that admit a transfer function completely described by their input-output behavior. Our objective is to identify and analyze the aforementioned classes, which exhibit unique characteristics related to separable systems. We aim to fit certain examples of automata/dynamical systems with new concepts. We observe that for a Discrete System or Automaton, the state set forms a group. Furthermore, there exists a natural near-ring for Separable Systems. Some substructures of this near-ring are generated by id. and a map from state set Q to itself if the state set Q is an abelian structure. It is interesting to note that Separable Systems themselves form a nearring with respect to parallel and series connections. We discuss certain results and provide examples to validate separable systems and the outcomes. This paper offers a theoretical and practical overview of dynamical systems in our daily lives. [ABSTRACT FROM AUTHOR]

In this paper, we use the results of a survey among Slovenian politicians in order to design an objective function for an optimal control problem with a macroeconometric model for fiscal policy in Slovenia that takes account of policy makers' preferences. The paper discusses three different scenarios in which the policy preferences revealed in interviews can be included in the objective functions of the control problems. These objective functions are then used to calculate optimal fiscal policies for the Slovenian economy until 2030. For this purpose, we utilise the macroeconometric model SLOPOL10 and the OPTCON2 algorithm. The results indicate qualitatively similar behaviour of the optimised dynamic system and a better performance (lower values of the loss due to deviation from "ideal" paths) from a ranking-based approach than from an ad-hoc assumption of policy makers' preferences. We sketch how to integrate the approach in a decision-support system for macroeconomic policy design. [ABSTRACT FROM AUTHOR]

This paper is concerned with the well-posedness and asymptotic behavior of solutions for the following extensible beam equation with non-local energy damping u tt + Δ 2 u - κ ϕ (‖ ∇ u ‖ 2 ) Δ u - φ (‖ Δ u ‖ 2 + ‖ u t ‖ 2) Δ u t + f (u) = h. More specifically, this is a complementary work to the paper by Sun and Yang (Discrete Contin Dyn Syst Ser B 27(6):3101–3129, 2022), where the authors consider this model assuming the hypothesis that φ ∈ C 1 (R +) with non-degenerate condition φ (s) > 0 , s ∈ R + . They prove the existence of strong global and exponential attractors and their robustness on the perturbed extensibility parameter κ . In this paper assuming φ (s) ⪆ γ s q which contemplates the degenerate condition φ (0) = 0 , we prove the existence of weak and regular solutions to the problem proposed and employing the method given in Temam (Springer-Verlag, New York, 1998) we show that the dynamic system (X , S t) given by the weak solutions of the problem has a compact global attractor in the weak topology of the phase space X. This class of nonlinear beams arising in connection with models for flight structures with non-local energy damping is proposed by Balakrishnan and Taylor (Proceedings Damping 89, Flight Dynamics Lab and Air Force Wright Aeronautical Labs, WPAFB, 1989). [ABSTRACT FROM AUTHOR]

The paper presents a method for determining the dynamic response of systems containing viscoelastic damping elements with uncertain design parameters. A viscoelastic material is characterized using classical and fractional rheological models. The assumption is made that the lower and upper bounds of the uncertain parameters are known and represented as interval values, which are then subjected to interval arithmetic operations. The equations of motion are transformed into the frequency domain using Laplace transformation. To evaluate the uncertain dynamic response, the frequency response function is determined by transforming the equations of motion into a system of linear interval equations. Nevertheless, direct interval arithmetic often leads to significant overestimation. To address this issue, this paper employs the element-by-element technique along with a specific transformation to minimize redundancy. The system of interval equations obtained is solved iteratively using the fixed-point iteration method. As demonstrated in the examples, this method, which combines the iterative solving of interval equations with the proposed technique of equation formulation, enables a solution to be found rapidly and significantly reduces overestimation. Notably, this approach has been applied to systems containing viscoelastic elements for the first time. Additionally, the proposed notation accommodates both parallel and series configurations of damping elements and springs within rheological models. [ABSTRACT FROM AUTHOR]

The balance between accuracy and computational complexity is currently a focal point of research in dynamical system modeling. From the perspective of model reduction, this paper addresses the mode selection strategy in Dynamic Mode Decomposition (DMD) by integrating an embedded fractal theory based on fractal dimension (FD). The existing model selection methods lack interpretability and exhibit arbitrariness in choosing mode dimension truncation levels. To address these issues, this paper analyzes the geometric features of modes for the dimensional characteristics of dynamical systems. By calculating the box counting dimension (BCD) of modes and the correlation dimension (CD) and embedding dimension (ED) of the original dynamical system, it achieves guidance on the importance ranking of modes and the truncation order of modes in DMD. To validate the practicality of this method, it is applied to the reduction applications on the reconstruction of the velocity field of cylinder wake flow and the force field of compressor blades. Theoretical results demonstrate that the proposed selection technique can effectively characterize the primary dynamic features of the original dynamical systems. By employing a loss function to measure the accuracy of the reconstruction models, the computed results show that the overall errors of the reconstruction models are below 5%. These results indicate that this method, based on fractal theory, ensures the model's accuracy and significantly reduces the complexity of subsequent computations, exhibiting strong interpretability and practicality. [ABSTRACT FROM AUTHOR]