Global Dynamics Of System Research Articles

Dynamic mode decomposition of GRACE satellite data

Advancements in satellite technology yield environmental data with ever improving spatial coverage and temporal resolution. This necessitates the development of techniques to discern actionable information from large amounts of such data. We explore the potential of dynamic mode decomposition (DMD) to discover the dynamics of spatially correlated structures present in global-scale data, specifically in observations of total water storage anomalies provided by GRACE satellite missions. Our results demonstrate that DMD enables data compression and extrapolation from a reduced set of dominant spatiotemporal structures. The accuracy of its predictions of global system dynamics is preserved in its reconstruction of local time series. These findings suggest potential uses of DMD in analysis of remote-sensing data for hydrologic applications.

Data-driven identification of stable sparse differential operators using constrained regression

Identifying differential operators from data is essential for the mathematical modeling of complex physical and biological systems where massive datasets are available. These operators must be stable for accurate predictions for dynamics forecasting problems. In this article, we propose a novel methodology for learning differential operators that are theoretically linearly stable and have sparsity patterns of common discretization schemes. These differential operators are obtained by solving a constrained regression problem, involving local constraints to ensure the linear stability of the global dynamical system. We further extend this approach for learning nonlinear differential operators by determining linear stability constraints for linearized equations around an equilibrium point. The applicability of the proposed method is demonstrated for both linear and nonlinear partial differential equations such as 1-D scalar advection-diffusion equation, 1-D Burgers equation and 2-D advection equation. The results indicated that solutions to constrained regression problems with linear stability constraints provide accurate and linearly stable sparse differential operators.

Bounds on the rates of statistical divergences and mutual information via stochastic thermodynamics.

Statistical divergences are important tools in data analysis, information theory, and statistical physics, and there exist well-known inequalities on their bounds. However, in many circumstances involving temporal evolution, one needs limitations on the rates of such quantities instead. Here, several general upper bounds on the rates of some f-divergences are derived, valid for any type of stochastic dynamics (both Markovian and non-Markovian), in terms of information-like and/or thermodynamic observables. As special cases, the analytical bounds on the rate of mutual information are obtained. The major role in all those limitations is played by temporal Fisher information, characterizing the speed of global system dynamics, and some of them contain entropy production, suggesting a link with stochastic thermodynamics. Indeed, the derived inequalities can be used for estimation of minimal dissipation and global speed in thermodynamic stochastic systems. Specific applications of these inequalities in physics and neuroscience are given, which include the bounds on the rates of free energy and work in nonequilibrium systems, limits on the speed of information gain in learning synapses, as well as the bounds on the speed of predictive inference and learning rate. Overall, the derived bounds can be applied to any complex network of interacting elements, where predictability and thermodynamics of network dynamics are of prime concern.

On classification of a 4D competitive LV system

This paper classifies the global dynamics of a 4D competitive Lotka-Volterra system (1.3) with two positive parameters k 1 , k 2 k_1,\ k_2 via carrying simplex. It is proved that the interior of the carrying simplex is filled with periodic orbits except equilibria and each interior trajectory is persistent and tends to either a periodic orbit or an equilibrium if k 1 / k 2 = 2 k_1/k_2=2 . Otherwise, the system admits two 2D carrying simplices Δ i \Delta _i on x 1 = i x_1=i for i = 0 , 1 i=0,\ 1 , which are filled with periodic orbits surrounding an equilibrium. All interior orbits go in the long run to Δ 1 \Delta _1 if k 1 / k 2 > 2 k_1/k_2>2 . If 0 > k 1 / k 2 > 2 0>k_1/k_2>2 , then the system admits a bistable structure: Δ 0 \Delta _0 and the equilibrium R 1 ( 1 + k 2 / k 1 , 0 , 0 , 0 ) R_1(1+k_2/k_1,\ 0,\ 0,\ 0) are locally asymptotically stable, the attracting set of Δ 1 \Delta _1 separates the attracting basins of Δ 0 \Delta _0 and R 1 R_1 .

Global phase space analysis for a class of single scalar field bouncing solutions in general relativity

We carry out a compact phase space analysis of a non-canonical scalar field theory whose Lagrangian is of the form F(X)-V(ϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(X)-V(\\phi )$$\\end{document} within general relativity. In particular, we focus on a kinetic term of the form F(X)=βXm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(X)=\\beta X^m$$\\end{document} (m≠1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m\ e 1/2$$\\end{document}) with power-law potential V0ϕn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V_0 \\phi ^n$$\\end{document} and exponential potential V0e-λϕ/MPl\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V_0 e^{-\\lambda \\phi /M_{Pl}}$$\\end{document} of the scalar field. The Cuscuton case m=1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m=1/2$$\\end{document} where the scalar field is non-dynamical is left out of consideration. The main aim of this work is to investigate the genericity of nonsingular bounce in these models and to investigate the cosmic future of the bouncing cosmologies when they are generic. A global dynamical system formulation that is particularly suitable for investigating nonsingular bouncing cosmologies is used to carry out the analysis. We show that when F(X)=βXm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(X)=\\beta X^m$$\\end{document} (β<0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta <0$$\\end{document}), nonsingular bounce is generic for a power law potential V(ϕ)=V0ϕn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V(\\phi ) = V_0 \\phi ^n$$\\end{document} only within the parameter range 12<m<1,n<2mm-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left\\{ \\frac{1}{2}<m<1,\\,n<\\frac{2\\,m}{m-1}\\right\\} $$\\end{document} and for an exponential potential V(ϕ)=V0e-λϕ/MPl\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V(\\phi ) = V_0 e^{-\\lambda \\phi /M_{Pl}}$$\\end{document} only within the parameter range 12<m≤1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left\\{ \\frac{1}{2}<m\\le 1\\right\\} $$\\end{document}. Except in these cases, nonsingular bounce in these models is not generic due to the non-existence of global past or future attractors. Our analysis serves to show the importance of a global phase space analysis to address important questions about nonsingular bouncing solutions, an idea that may and must be adopted for such solutions even in other theories.

Global dynamics of 3D cooperative Lotka-Volterra system with the identical intrinsic growth rate

In this paper, we complete the classification on global topological structures of the three-dimensional cooperative Lotka-Volterra system with the identical intrinsic growth rate inside the Poincaré compactification of the positive octant of R3. Precisely, with the help of the replicator equations it is proved that this kind of system can have exactly 8 topologically different phase portraits. As a consequence, we obtain the necessary and sufficient conditions for the system to be bounded in the positive octant.

Assessing the progress toward achieving energy‐ and climate‐related sustainable development goals under four global energy transition outlooks

AbstractClimate change is one of the greatest challenges in achieving the United Nations Sustainable Development Goals (SDGs), underscoring the critical need for energy transitions to mitigate the climate crisis. The achievement of two energy‐ and climate‐focused SDGs—SDG 7 (affordable and clean energy) and SDG 13 (climate action)—remains uncertain under potential future global energy transition outlooks. This study evaluates the progress toward achieving SDGs 7 and 13 by 2050 under four representative energy transition outlooks through 14 performance indicators derived from a global system dynamics model. Our results reveal a progressive trend in achieving SDGs 7 and 13 under these energy transition outlooks. The overall progress scores toward these two SDGs are estimated as 16.23% in 2030 and 20.06% in 2050 under the most conservative outlook and 65.35% in 2030 and 88.24% in 2050 under the most radical outlook. Although energy transitions contribute to achieving SDGs 7 and 13, our analysis indicates that the world is far off‐track in achieving these SDGs by relying solely on the implementation of energy transition policies. We further suggest promising measures from both the energy sector and other vital sectors to facilitate progress toward achieving the two SDGs.

Extracting transmission and recovery parameters for an adaptive global system dynamics model of the COVID-19 pandemic (lay summary)&amp;nbsp;

Extracting transmission and recovery parameters for an adaptive global system dynamics model of the COVID-19 pandemic (lay summary)&amp;nbsp;

Threshold dynamics of a stochastic single population model with Allee effect

A stochastic single species population model with Allee effect is considered in this paper. By using the theory of Random Dynamical System (RDS), the complete classification of the global dynamics of stochastic system is given. The theoretical results show that the dynamics of the system is completely determined by the threshold λ=2r−σ2: if λ≤0, the population will extinct, i.e., the solutions of the model will go to zero; if λ>0, the population is permanent. Moreover, the transition probabilities of the solutions weakly converge to the unique stationary distribution and the explicit density function of the stationary distribution is given.

Global dynamics of a ring-tethered three-satellite system in any plane

Global dynamics of a ring-tethered three-satellite system in any plane

Optimal consensus control for multi-satellite assembly in elliptic orbit with input saturation

This paper presents an optimal control design method for multi-satellite assembly in an elliptic orbit in close proximity operations considering input saturation constraints. Tschauner–Hempel (T–H) equations are utilized to model the relative motion dynamics of the satellites in the Local Vertical Local Horizontal (LVLH) frame of the target satellite, where every satellite in the assembly is modeled as a point mass. The communication topology between the satellites in the assembly is modeled using graph theory, where the graph has several nodes representing the satellites and several edges representing the data exchange direction. It is assumed that every satellite exchanges its states with a few neighbors in the team, where the neighbors of every satellite are prespecified and do not change during the mission. This graph is utilized to construct the global dynamic model of the assembly, in which every node is represented by the dynamic model of a single satellite. The local control law, which is applied to every satellite in the assembly, consists of a state feedback gain and a coupling gain. The state feedback gain is designed using the discrete-time periodic Riccati equation to guarantee the local stability of every satellite separately, while the coupling gain is selected to satisfy the Lyapunov condition to guarantee the global stability of the assembly. The invariant-set method is utilized to prove the stability of the global dynamic system that is subjected to symmetric input saturation. The precision and optimality of the proposed control law are successfully demonstrated by numerical nonlinear simulations in a MATLAB environment for a cubic formation satellite assembly.

Global dynamics analysis of a water hyacinth fish ecological system under impulsive control

Control of a water hyacinth-fish ecological system is required for a healthy and sustainable environment. This paper aims to investigate the global dynamics of a water hyacinth fish ecological system under ratio-dependent state impulsive control. First, we study the positivity and boundedness of the solution of the controlled system. By studying the local stability of the equilibrium, we find that the system has two situations. One is that there are two equilibria, namely a saddle point and a boundary equilibrium. In the second case, there are four equilibria, namely, two saddle points, a boundary equilibrium, and a focus point. For the first case, when we select an appropriate ratio-dependent control threshold, the trajectory will globally converge to the boundary equilibrium. For the second case, when the control line is located below the focus point, by using Poincare mapping method, flip bifurcation theory, and vector field analysis techniques, we find that the solution of the controlled system either globally converges to the boundary equilibrium, order-1 periodic solution, or order-2 periodic solution under certain conditions. When the control line is located above the focus point, the solution of the controlled system either globally converges to the focus point, order-1 or order-2 periodic solution. Finally, we use examples to verify the correctness and validity of the theoretical results.

The first International Conference on Mechanical System Dynamics grandly convened in Nanjing, China

The first International Conference on Mechanical System Dynamics grandly convened in Nanjing, China

Global dynamics of a Filippov epidemic system with nonlinear thresholds

Due to the intermittency of prevention and control measures, the right-hand function of the dynamic model describing the spread of infectious disease is often induced to be nonsmooth, which can be formulated by employing Filippov systems and have been widely studied recently. Note that these systems only consider the number of infected individuals as the switching threshold. However, infectious disease control depends not only on the number of infected individuals, but also on the change rate of infected individuals. To address this, we propose a Filippov system with media-influenced nonlinear thresholds which integrate the change rate of infected individuals into the threshold strategy. The main results reveal that the proposed threshold strategy can induce the complex dynamic behavior, including multiple sliding segments and pseudo-equilibrium. Furthermore, our main results show that variations of threshold (ET) and the nonlinear threshold control strategy not only lead to rich dynamics including bistability, but also have important implications for disease control.

A quasi-static contact model for global dynamic simulation of multibody system with contact-impact

The global impact dynamics of multibody system is challenging due to the multi-scale characteristics of slow-changing non-contact process and fast-changing impact process. To solve the contradiction between the impact accuracy and the global simulation efficiency, a novel quasi-static contact model is proposed where the local contact domain is finely discretized and the energy loss caused by elastoplasticity is considered, and the real-time force-displacement interaction is established to execute the global integration capably. Through the experimental case of flexible pendulum impact, the proposed model is compared with measurements and existing methods, including impulse method, continuous contact force method and nonlinear finite element method. It is shown that the impulse method and continuous contact force method are both sensitive to the coefficient of restitution, yielding uncertain results. The nonlinear finite element method can accurately describe the impact process, but its calculation scale is too large to apply to the global simulation. The quasi-static model can accurately describe the response of the global process and does not rely on artificial selection of any parameters, and the calculation efficiency is greatly improved compared with the nonlinear finite element method.

Novel results on attractivity of a neoclassical growth system incorporating multiple pairs of time-varying delays

In this paper, we analyze the global dynamics of a neoclassical growth system incorporating patch structure and multiple pairs of time-varying delays. First, we derive the global existence, positiveness and boundedness of solutions for the addressed system. Then, by employing some novel differential inequality analyses and the fluctuation lemma, both delay-independent and delay-dependent criteria are established to ensure that all solutions are convergent to a unique positive equilibrium point vector, which does not possess the same components. Our results supplement and improve some existing results. Ultimately, some numerical examples are afforded to prove the effectiveness and feasibility of the theoretical findings.

Cosmological global dynamical systems analysis

We consider a dynamical systems formulation for models with an exponential scalar field and matter with a linear equation of state in a spatially flat and isotropic spacetime. In contrast to earlier work, which only considered linear hyperbolic fixed point analysis, we do a center manifold analysis of the non-hyperbolic fixed points associated with bifurcations. More importantly though, we construct monotonic functions and a Dulac function. Together with the complete local fixed point analysis this leads to proofs that describe the entire global dynamics of these models, thereby complementing previous local results in the literature.

Comparison of Global and Regional Compliance-Guided Positive End-Expiratory Pressure Titration on Regional Lung Ventilation in Moderate-to-Severe Pediatric Acute Respiratory Distress Syndrome.

PurposeTo investigate the difference in the positive end-expiratory pressure (PEEP) selected with chest electrical impedance tomography (EIT) and with global dynamic respiratory system compliance (Crs) in moderate-to-severe pediatric acute respiratory distress syndrome (pARDS).MethodsPatients with moderate-to-severe pARDS (PaO2/FiO2 < 200 mmHg) were retrospectively included. On the day of pARDS diagnosis, two PEEP levels were determined during the decremental PEEP titration for each individual using the best compliance (PEEPC) and EIT-based regional compliance (PEEPEIT) methods. The differences of global and regional compliance (for both gravity-dependent and non-dependent regions) under the two PEEP conditions were compared. In addition, the EIT-based global inhomogeneity index (GI), the center of ventilation (CoV), and standard deviation of regional delayed ventilation (RVDSD) were also calculated and compared.ResultsA total of 12 children with pARDS (5 with severe and 7 with moderate pARDS) were included. PEEPC and PEEPEIT were identical in 6 patients. In others, the differences were only ± 2 cm H2O (one PEEP step). There were no statistical differences in global compliance at PEEPC and PEEPEIT [28.7 (2.84–33.15) vs. 29.74 (2.84–33.47) ml/cm H2O median (IQR), p = 0.028 (the significant level after adjusted for multiple comparison was 0.017)]. Furthermore, no differences were found in regional compliances and other EIT-based parameters measuring spatial and temporal ventilation distributions.ConclusionAlthough EIT provided information on ventilation distribution, PEEP selected with the best Crs might be non-inferior to EIT-guided regional ventilation in moderate-to-severe pARDS. Further study with a large sample size is required to confirm the finding.

Global dynamics of a generalist predator–prey model in open advective environments

This paper deals with a system of reaction-diffusion-advection equations for a generalist predator-prey model in open advective environments, subject to an unidirectional flow. In contrast to the specialist predator-prey model, the dynamics of this system is more complex. It turns out that there exist some critical advection rates and predation rates, which classify the global dynamics of the generalist predator-prey system into three or four scenarios: (1) coexistence; (2) persistence of prey only; (3) persistence of predators only; and (4) extinction of both species. Moreover, the results reveal significant differences between the specialist predator-prey system and the generalist predator-prey system, including the evolution of the critical predation rates with respect to the ratio of the flow speeds; the take-over of the generalist predator; and the reduction in parameter range for the persistence of prey species alone. These findings may have important biological implications on the invasion of generalist predators in open advective environments.

Improving the Forecasting of Winter Wheat Yields in Northern China with Machine Learning–Dynamical Hybrid Subseasonal-to-Seasonal Ensemble Prediction

Subseasonal-to-seasonal (S2S) prediction of winter wheat yields is crucial for farmers and decision-makers to reduce yield losses and ensure food security. Recently, numerous researchers have utilized machine learning (ML) methods to predict crop yield, using observational climate variables and satellite data. Meanwhile, some studies also illustrated the potential of state-of-the-art dynamical atmospheric prediction in crop yield forecasting. However, the potential of coupling both methods has not been fully explored. Herein, we aimed to establish a skilled ML–dynamical hybrid model for crop yield forecasting (MHCF v1.0), which hybridizes ML and a global dynamical atmospheric prediction system, and applied it to northern China at the S2S time scale. In this study, we adopted three mainstream machining learning algorithms (XGBoost, RF, and SVR) and the multiple linear regression (MLR) model, and three major datasets, including satellite data from MOD13C1, observational climate data from CRU, and S2S atmospheric prediction data from IAP CAS, used to predict winter wheat yield from 2005 to 2014, at the grid level. We found that, among the four models examined in this work, XGBoost reached the highest skill with the S2S prediction as inputs, scoring R2 of 0.85 and RMSE of 0.78 t/ha 3–4 months, leading the winter wheat harvest. Moreover, the results demonstrated that crop yield forecasting with S2S dynamical predictions generally outperforms that with observational climate data. Our findings highlighted that the coupling of ML and S2S dynamical atmospheric prediction provided a useful tool for yield forecasting, which could guide agricultural practices, policy-making and agricultural insurance.