Dynamics Of Coupled System Research Articles

Dynamics analysis of a rigid-flexible-liquid coupled satellite antenna system via absolute nodal coordinate formulation curvature continuity constraints

Typically, Euler and Lagrangian approaches are primarily used in fluid dynamics and multibody system (MBS) dynamics models, respectively. Absolute nodal coordinate formulation (ANCF), as a Lagrangian nonlinear finite element method (FEM), can effectively handle large deformation problems and incorporate the arbitrary Lagrange-Eulerian (ALE) method for fluids turbulence and breaking. Therefore, we have established a rigid-flexible-liquid coupled satellite antenna system dynamics model via ANCF. Navier-Stokes equations and virtual work principle are applied to formulate the fluid-structure interaction (FSI) dynamics equations. A penalty function is used to describe liquid incompressibility. Bi-directional FSI effects are solved simultaneously and brick fluid element elastic force is validated with reference experiments. Moreover, we introduce curvature continuity constraints to make the liquid free surface continuous. Results indicate that curvature continuity constraints can smoother liquid free surface and eliminate the protrusions and depressions caused by assembling brick fluid elements. Furthermore, we achieve simulation results consistent with reference experiments by using fewer elements with curvature continuity constraints. In addition, due to bi-directional FSI effects, liquid sloshing will magnify satellite antenna vibrations and simultaneously oscillate the advancing tank.

Synchronization and chaos control in coupled Non-identical systems: application in Wind Turbine-Grid coupled power systems

The increasing number of renewable energy systems coupled to the grid can lead to electrical energy losses when the currents or voltages of the two systems are not synchronized. Many mathematical models have investigated the phenomenon of synchronization in coupled systems. Here, we mathematically model the dynamics of a wind turbine-grid coupled system as a periodically driven Duffing resonator coupled to a Van der Pol oscillator with both position and velocity coupling. We consider the fluctuating nature of the wind as the only external driving force. We integrate the coupled system of equations under different coupling strengths and driven frequencies using the Runge-Kutta method of order 4(RK4). The result suggests that synchronization can be achieved at higher coupling strengths even with small values of the driven frequencies than at lower coupling strengths. At higher values of the driven frequency, the system exhibits chaotic behavior for both strong and weak couplings but with synchronization maintained only for the strong coupling case. Our results suggest chaos and synchronization can be controlled in this system by turning appropriate parameters.

Strong Resemblance between Surface and Deep Zonal Winds inside Jupiter Revealed by High-degree Gravity Moments

Jupiter’s atmosphere interior is a coupled fluid dynamical system strongly influenced by the rapid background rotation. While the visible atmosphere features east–west zonal winds on the order of ∼100 m s−1, zonal flows in the dynamo region are significantly slower, on the order of ∼cm s−1 or less, according to the latest magnetic secular variation analysis. The vertical profile of the zonal flows and the underlying mechanism remain elusive. The latest Juno radio tracking measurements afforded the derivation of Jupiter’s gravity field to spherical harmonic degree 40. Here, we use the latest gravity solution to reconstruct Jupiter’s deep zonal winds without a priori assumptions about their latitudinal profile. The pattern of our reconstructed deep zonal winds strongly resemble that of the surface wind within ±35° latitude from the equator, in particular the northern off-equatorial jet (NOEJ) and the southern off-equatorial jet. The reconstruction features larger uncertainties in the southern hemisphere due to the north–south asymmetric nature of Juno's trajectory. The amplitude of the reconstructed deep NOEJ matches that of the surface wind when the wind is truncated at a depth ∼2500 km, and becomes twice that of the surface wind if the truncation depth is reduced to ∼1500 km. Our analysis supports the physical picture in which a prominent part of the surface zonal winds extends into Jupiter’s interior significantly deeper than the water cloud layer.

Stationary states and switching dynamics of the self-defocusing nonlinear coupled system with PT-symmetric [formula omitted]-wavenumber Scarf II potential

The stationary states and switching dynamics of the parity-time (PT) symmetric coupled system with k-wavenumber Scarf II potential in the self-defocusing nonlinear regime have been analysed. The eigenmodes with central peaks are evolved in the linear regime, whereas those with central dips are evolved in the defocusing nonlinear regime, for ground, 2nd, and 4th excited states. The threshold condition of the PT-symmetry breaking and the effect of coupling, self-defocusing nonlinearity, and width of the potential on the high and low-frequency modes of the ground and excited states have been analysed. The stability of the eigenmodes is verified using the linear stability analysis. The power-switching dynamics between the gain and lossy channels of the system has been analysed. The input power-dependent switching and the effects of gain/loss and potential width on the switching are discussed.

Impact of wheel profile evolution on the lateral motion characteristics of a high-speed vehicle navigating through turnout

The wheel-rail contact asymmetry on the left and right sides of the wheelset while navigating high-speed vehicles through turnouts can lead to lateral motion of the wheelset, ultimately resulting in substantial vibrations in the vehicle system. This study employs the trace method to examine the changing pattern of the wheel-rail equivalent conicity in the turnout area as the wheel profile evolves. A coupled system dynamics model containing flexible turnouts is established. Specifically, the model examines the lateral position of wheel-rail contact points, the lateral motion of the wheelset, and the lateral vibration acceleration of the vehicle system. The study indicates that the lateral motion characteristics of high-speed trains passing through turnouts are influenced by the degree of wheel wear. When the wheels are slightly worn (for mileage below or equal to 100,000 km), the lateral dynamic responses of the vehicle system are affected by the inherent structure of the turnout. When the wheels are severely worn (for mileage above or equal to 150,000 km), the lateral dynamic response of the vehicle system is no longer affected by the inherent structure of the turnout.

Development of a behaviour pattern-based testing approach for coupled socioeconomic and environmental models

Understanding the interactions between human and environmental systems is key to sustainable environmental management. Dynamically Coupled Socioeconomic system dynamics models integrated with physically-based Environmental Models (DCSEMs) are promising tools to appropriately capture the non-linear relationships between complex socioeconomic and biophysical systems, thereby supporting sustainable environmental management. However, existing approaches for testing integrated models are commonly based on the point-to-point analysis of model outputs, which is not suitable for DCSEMs that are behaviour pattern oriented. Consequently, the lack of well-defined behaviour pattern-based approaches has limited the adaptability of DCSEMs. To address this gap, this study proposes a novel behaviour pattern-based model testing approach that includes global sensitivity analysis (GSA), auto-calibration algorithms, and evaluation to assess behaviour pattern similarities between model outputs and real-world trends. The proposed approach is demonstrated through a real-world case study, in which an existing DCSEM is calibrated and evaluated to simulate water table depth in the Rechna Doab region of Pakistan. Compared to the conventional numerical point approach, the proposed approach is better suited for DCSEMs, as it replicates observed system behaviour patterns (as opposed to observed point values) over time. Furthermore, the outcomes of the Theil inequality statistical analysis and parameter distribution analysis provide evidence that the suggested approach is effective in testing and improving the performance of the DCSEM by capturing the spatial heterogeneity within the study area. The proposed behaviour-pattern testing procedure is a useful approach for model testing in data-limited, spatially-distributed DCSEMs.

Land Use Change and Landscape Ecological Risk Prediction in Urumqi under the Shared Socio-Economic Pathways and the Representative Concentration Pathways (SSP-RCP) Scenarios

Understanding land use/cover change (LUCC) and landscape ecological risk change in the context of future climate warming can help adjust socio-economic development policies, optimize regional ecological security patterns, and promote green and low-carbon development on the one hand and provide important supplements and improvements for research in related fields on the other. Taking Urumqi as the study area, based on the Coupled Model Intercomparison Project Phase 6 (CMIP6) multi-modal ensemble data, we used the coupled system dynamics (SD) model and patch-generation land use simulation (PLUS) model to simulate land use change under three SSP-RCP scenarios in 2020–2060, and we predicted trends of landscape ecological risk change in this 40-year period by using the landscape ecological risk index (LERI). The results indicate that woodland and grassland significantly increase under the SSP126 scenario. Unused land is larger in the SSP245 scenario. The expansion trend of construction land toward cultivated land is most obvious in the SSP585 scenario; additionally, the area of water increases more distinctly in this scenario. The overall landscape ecological risk under the three SSP-RCP scenarios is reduced to different degrees; in particular, the risk level of urban built-up areas and nature reserves decreases remarkably, and the area of the highest risk zones of unused land is also gradually narrowed. By 2060, the average LERI under the SSP126 scenario is the lowest. The study findings can help relevant departments formulate reasonable urban development plans, which are of great theoretical and practical significance for guaranteeing regional ecological security.

Subseasonal-to-seasonal prediction of arctic sea ice Using a Fully Coupled dynamical ensemble forecast system

With the opening of Arctic passage for maritime transportation under global warming, accurate prediction of Arctic sea ice (ASI) on subseasonal-to-seasonal (S2S) timescales becomes increasingly crucial for the economy and society but challenging. This study examined the S2S hindcast skills of monthly ASI during 1992–2019 using Flexible Global Ocean-Atmosphere-Land System, Finite-Volume version 2 (FGOALS-f2), a global coupled model that includes an interactive dynamical sea ice component. Firstly, the prediction system can accurately capture the seasonal cycle of Arctic sea ice extent (SIE). Still, it slightly overestimates SIE in March–June and significantly underestimates SIE in August–December. Meanwhile, the declining trend of SIE is underestimated in predictions for all target seasons, particularly for spring. Secondly, relatively high skills with an average ACC of 0.44 are found in predicting monthly SIE anomalies (SIEA) after removing the long-term linear trend at a one-to-six-month lead. However, the one-to-six-month lead prediction skills in April drop significantly by 36% when the interdecadal variation is removed. We find that the variation of April SIEA after removing the linear trend is dominated by the Pacific Decadal Oscillation (PDO), which can be better predicted than interannual variability ahead of subseasonal timescales. Unlike the SIE error-based metrics considered in previous studies, the one-to-three-month lead prediction in FGOALS-f2 shows significantly better performance in predicting the spatial distribution of September ASI for extreme years compared to normal years. Finally, the skill for predicting minimum SIEA in FGOALS-f2 is considerably higher at a three-to-six-month lead than anomaly persistence, indicating the advantage of this dynamical prediction system at a longer lead time.

Safety of an express freight train running over a bridge in crosswind

Owing to the blunt car body and high design speed of express freight trains, the running safety is significantly affected by crosswinds when the train runs over a bridge; moreover, severe accidents, such as derailment or overturning may occur. Therefore, adequate measures should be adopted to avoid the occurrence of such accidents. In this study, a finite element model of the train, ballastless track, and parameterized 5-span simply supported girder bridge along with modal superposition method are adopted to establish the train-track-bridge coupling dynamic system. Numerical simulation of stochastic wind speed, wind tunnel tests, and computational fluid dynamics (CFD) simulation of vehicle-bridge scale model were conducted to calculate the wind load acting on the train and bridge. The dynamic responses of the bridge and train were evaluated to present the diagrams of wind and train speed limits for safe operation. The results indicated that the running safety of the vehicle declined with the wind and train speeds, and the wheel unloading rate was the most sensitive to wind speed. For safe operation, the train speed must be restricted if the mean wind speed is greater than 22.7 m/s, and an extreme scenario of derailment may occur for a mean wind speed of 34.0 m/s. In addition, the wind speed limit should be appropriately adjusted and improved according to the pier height of the bridge and terrain category. This research provides a theoretical basis and data support for the assessment of safety of express freight trains in actual operation.

A Multi-Period Charging Service Pricing Game for Public Charging Network Operators Considering the Dynamics of Coupled Traffic-Power Systems

The proliferation of electric vehicles (EVs) couples the operations of traffic systems and power systems, necessitating the interdependent traffic-power modeling to optimize the on-road EV charging decisions. In this paper, the multi-period charging service pricing interactions between multiple charging network operators (CNOs) are discussed considering the dynamics of traffic-power systems. A multi-period user equilibrium model considering mixed vehicle types is formulated to describe the possible vehicle trip transitions between different periods in urban transportation network. For the power distribution network, a convexified multi-period AC optimal power flow model is adopted for local electricity market clearing. With the dynamics of traffic-power systems, the pricing interaction between multiple CNOs is a non-cooperative game. We analyze the existence of Nash Equilibrium with fixed-point theory, and propose an iterative method based on the best response strategy to find <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon$</tex-math> </inline-formula> -Nash Equilibrium. Numerical studies based on an interdependent power-traffic system consisting of two 18-node power distribution networks and one revised Nguyen-Dupuis transportation network demonstrate that with the proposed CNOs’ charging pricing strategy, the CNOs’ service profits can increase by 1%-3% while the PDNs’ operation costs decrease about 1%-2% for the interdependent traffic-power system.

Analytical Calculation and Rapid Simulation of Survival Signatures in Dynamic Fault Trees With Priority-AND Gates

Many practical systems are often involved in sequence-dependent failure behaviors. The efficiency of analyzing these dynamic systems is limited by addressing sequential failure events (SFEs). The survival signature method has the potential to address this issue. However, the survival signature cannot be applied directly due to the existence of SFEs. In this article, the adapted survival signature-based methods are developed for the rapid analysis of dynamic systems modeled by dynamic fault trees with priority- <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">and</small> gates. First, we deduce the probabilistic expressions of SFEs under the survival signature paradigm using conditional probability. Second, an analytical method for accurately computing the survival signatures of dynamic systems is proposed. Third, for large-scale and highly coupled dynamic systems, a semianalytical method is proposed to obtain the survival signature through simulating the Boolean states of SFEs under given components’ state. Several numerical and practical engineering cases are examined to highlight the superiority of the proposed methods compared with the sequential binary decision diagram method and coarse Monte Carlo simulation.

Coupling System Dynamics Model of Cross Border Logistics and Ecological Environment Based on the Sustainable Perspective of Global Value Chain

International import and export trade, along with cross-border logistics management, plays a pivotal role in the era of globalization, driving the development of the global economy and fostering international trade prosperity. Nevertheless, the continuous growth of the global economy has also brought forth fresh challenges to the ecological environment posed by cross-border logistics activities. Against this backdrop, this paper begins by analysing the correlation between international trade and logistics activities. The study reveals a positive response relationship between the total volume of international import and export trade and cross-border logistics, demonstrating a positive correlation. Subsequently, the impact of international import and export trade, as well as cross-border logistics, on the ecological environment is discussed, underscoring the significance of implementing ecological environment monitoring. Taking into account the environmental impact of cross-border logistics activities, an integrated system is proposed and designed to enhance cross-border logistics efficiency while considering environmental protection and sustainable development. This system encompasses real-time monitoring, data collection, threat, and risk assessment. This study makes a clear contribution to research on green innovation and environmental protection within the context of cross-border logistics. It offers a different perspective on the integration of cross-border logistics management and the ecological environment, deepens understanding of environmental protection innovation strategies and cross-border logistics management from the perspective of sustainable development. Furthermore, it provides valuable management insights for related enterprises to balance development and environmental protection. Additionally, it sheds light on the international impact of import and export trade, offering crucial inspiration and theoretical references for decision-making.

Large-scale real-life implementation of technology-enabled care to maximize hospitals' medical surge preparedness during future infectious disease outbreaks and winter seasons: a viewpoint.

Hospitals can be overburdened with large numbers of patients with severe infectious conditions during infectious disease outbreaks. Such outbreaks or epidemics put tremendous pressure on the admission capacity of care facilities in the concerned region, negatively affecting the elective program within these facilities. Such situations have been observed during the recent waves of the coronavirus disease pandemic. Owing to the imminent threat of a "tripledemic" by new variants of the coronavirus disease (such as the new Omicron XBB.1.16 strain), influenza, and respiratory syncytial virus during future winter seasons, healthcare agencies should take decisive steps to safeguard hospitals' surge capacity while continuing to provide optimal and safe care to a potentially large number of patients in their trusted home environment. Preparedness of health systems for infectious diseases will require dynamic interaction between a continuous assessment of region-wide available hospital capacity and programs for intensive home treatment of patients who can spread the disease. In this viewpoint, we describe an innovative, dynamic coupling system between hospital surge capacity and cascading activation of a nationwide system for remote patient monitoring. This approach was developed using the multi-criteria decision analysis methodology, considering previously published real-life experiences on remote patient monitoring.

A modelling methodology of the axle box bearing-vehicle coupled system dynamics

The axle box bearing serves as a critical rotational component for high-speed trains. Thus, it is of great significance to obtain accurate loading conditions for axle box bearings for its reliability design. In this study, a bearing-vehicle coupled system dynamic model, consisting of an equivalent bearing model characterized by the time-varying stiffness in the bearing, a nonlinear high-speed train dynamic model, and a slab track model, is developed. The validity of the proposed coupled dynamic model is demonstrated by comparing the simulated results with those obtained in a field test and the literature, respectively. Subsequently, the influence of long- and short-wavelength irregularities on the dynamic responses of bearings is investigated using the proposed coupled model in terms of dynamic loads of the axle box bearing. The results obtained by the proposed model are further compared with those calculated using a traditional vehicle dynamic model that represents the bearing as a revolute joint, so as to illustrate the advantages of the proposed model. The results suggest that the loading responses of the bearing calculated by the two models exhibit differences, which are simultaneously related to the structural damping of the bearing and the mode frequency change of the system.

Area-based scenario development in land-use change modeling: A system dynamics-assisted approach for mixed agricultural-residential landscapes

This study aimed to enhance land use and land cover (LULC) change models by addressing their main limitations, which include the lack of accountability and temporal stability of driving forces. Additionally, the study aimed to create area-based scenarios to forecast future LULCs, rather than solely relying on distribution-based scenarios. To accomplish this goal, the study developed a coupled System Dynamics (SD) and Cellular Automata (CA) modeling system to simulate possible LULC changes in the Gavkhooni Basin, central Iran. The study utilized LULC maps from Landsat images in 2001, 2011, and 2021 to analyze spatio-temporal land use changes in the region. Agricultural and residential transition suitability layers were produced using a spatial Multi-Criteria Evaluation procedure and applied to inform the CA model in the proper allocation of LULC changes. Three interconnected water supply, agricultural, and residential area projection subsystems were developed using system dynamics method to determine land requirements for LULC conversions from 2020 to 2041, taking into account factors such as water availability, land suitability, agricultural labor force, and economic development. Ten scenarios were developed based on changes in the key variables affecting the limiting factors, such as climatic conditions and water management policies, to project agricultural and residential areas in the future. The CA's spatial allocation informed by transition suitability layers was found to be satisfactory with a Kappa-location value of 0.85. The subsystems were competent in projecting water supply with Mean Absolute Error (MAE) values of 6.57% and the dynamics of agricultural and residential areas with MAE values of 2.94%, whereas those of the Markovian Chain model were found to be 23.02% and 7.5% for agricultural and residential areas, respectively. The study found that available agricultural areas varied significantly between 86.53 and 1480 sq.km under different climatic conditions, irrigation efficiency, and agricultural water assignment coefficients between 2024 and 2033. Residential area demand was found to be increasing with different rates under the scenarios between 47.40 and 73.01 sq.km. The SD-CA coupled framework presented in this research can be viewed as a decision support system to develop compensatory strategies for better management and planning of agricultural and residential lands.

Dynamically coupling system dynamics and SWAT+ models using Tinamït: application of modular tools for coupled human–water system models

Abstract. Participatory water resource management requires modeling techniques that are accurate and flexible yet stakeholder-friendly. While different modeling frameworks offer advantages and disadvantages, system dynamics (SDs) models have seen sustained use as a stakeholder-friendly approach for participatory water resource modeling. Physically based models (e.g., SWAT+) have seen sustained use to model the hydrological components of water systems. Proposed as a way to combine the relative strengths of both modeling paradigms, model coupling allows researchers to, for example, build participatory SD models with stakeholders, while delegating the hydrological components of the overall model to an external hydrological model. Recently developed to facilitate model coupling, the Tinamït Python package presents an extensible, outward-facing application programming interface (API). It allows for the development of extensions (wrappers) that expand compatibility with different physically based models. However, no watershed hydrological model has yet been connected to this API. In the present study, a socket and JavaScript Object Notation (JSON)-based communication protocol was developed with the goal of facilitating the coupling of models written in languages such as Fortran. This novel protocol served to develop a Tinamït-compatible wrapper for the hydrological model SWAT+, allowing it to be coupled to human–water SD models. The novel coupling protocol was then applied to a case study of Tanzania's Usa river catchment. This approach provides the modeler with the benefits of both physically based and SD models, thereby allowing the detection of potentially far-reaching effects of policy-makers' decisions.

Image-Based Visual Servoing of Quadrotors to Arbitrary Flight Targets

Visual servoing of Unmanned Aerial Vehicles (UAVs) has achieved satisfactory performance in fixed and planar motion targets. Due to highly coupled system dynamics and the sensitivity of the target image to aircraft attitude, the problem for chasing free-flying targets remains challenging. In this paper, a vision-based algorithm is designed for controlling an UAV while tracking an intruder flying arbitrarily in 3D space. Image-based visual servoing is used to design controllers that depend directly on errors in image plane. Specifically, a virtual camera approach is adopted to decouple the UAV dynamics by compensating the pitch and yaw, and an improved image error term is proposed to reduce the impact of the UAV rotation on error signals in the process of tracking, thus a simplified control design is achieved, and the stability of the visual servo system is guaranteed. Comparison and ablation experiments in both simulated and real environments are provided to verify the effectiveness of the proposed method.

Dynamic Analysis of the High Speed Train–Track Spatial Nonlinear Coupling System Under Track Irregularity Excitation

Track irregularity is the main factor that affects the safety and comfort of high-speed railway. It is important to study the influence of the track irregularity on the safety service of high speed train–track coupling system. In this paper, a vehicle–track spatial nonlinear coupled system dynamics model is developed with FEM. The model includes vehicle subsystem and track subsystem, which are coupled by wheel–rail interface. The vehicle subsystem is a 31-DOF spatial vehicle model, and the track subsystem is a three-dimensional slab track model composed of the rail, rail pad and track slab. Considering wheel tread profile and rail head profile, the wheel–rail spatial contact geometry relationship is established, and the “Trace method” and the “Minimum distance method” are used to search for wheel–rail contact points. Considering the nonlinear contact between the wheel and the rail, a numerical approach is presented, where the “Trace method” is embedded into the algorithm for solving the vehicle–track nonlinear coupling dynamics equation by cross iteration, realizing searching the wheel–rail contact points and solving the vehicle–track nonlinear coupling equation simultaneously, which greatly improves the efficiency of numerical analysis. As application examples, the dynamic responses of a high speed train–track spatial nonlinear coupled system excited by the track V-shaped local profile irregularity and the track torsional irregularity are analyzed. The results show that the algorithm is effective in solving the vehicle–track spatial nonlinear coupled system dynamics problem, and the track irregularity has significant influence on the dynamic response of vehicle and track structure.

Sustainable Coupling Coordination and Influencing Factors of Sports Facilities Construction and Social Economy Development in China

Sports facilities are a crucial physical safeguard and means of sustaining sporting activities. The steady and healthy development of sports facilities can promote the sustainable development of the social economy. In order to explore the coordination status and influencing factors between sports facilities construction and the social economy, this paper built a coupling coordination evaluation index system and dynamic factor index system for the sports facilities construction and social economy development by using the entropy method, coupling coordination model and random effect model. This paper assessed the comprehensive level, coupling coordination relationship, and influencing factors of the sports facilities and social economy development of nine cities in the Fujian Province across China from 2016 to 2020. The results show the overall level of sports facilities construction in Fujian is better than the social economy development, and the two systems are interacting with each other. The level of coupling and coordination gradually changes from good coordination to quality sustainable coordination. The coupling coordinated relationship between the two systems is developing in a positive way. In addition, industrial development, the level of urban development, and environmental development as influencing factors have a clear positive effect on the degree of coupling coordination. This study provides several recommendations for cities to achieve sustainable coordinated development. This paper also may provide a direction and path for future research.

Autoregulation of excitation-Ca2+ signaling-contraction and arrhythmogenesisin cardiomyocyte under mechanical load.

The heart pumps blood into circulation against the mechanical load from vascular resistance and actively regulates cardiomyocyte contraction to compensate for load changes. We conducted Cell-in-Gel experiments to decipher the mechano-chemo-electro-transduction (MCET) mechanisms that transduce the mechanical load during cell contraction to regulate the excitation-Ca2+ signaling-contraction (E-C) coupling. Our experimental studies reveal that MCET increases the L-type Ca2+ current and action potential duration, which increases the Ca2+ entry during the cardiac cycle; increases the diastolic SR Ca2+ content, the systolic SR Ca2+ release, and the Ca2+ uptake; and increases the cytosolic Ca2+ transient, resulting in MCET-Ca2+ gain. The MCET-Ca2+ gain enhances contractility in response to increased load. Hence, MCET provides feedback loops in the E-C coupling system, which may enable autoregulation of the dynamic system when mechanical load changes. Based on experimental data, we developed quantitative models to incorporate the MCET feedback loops into the E-C coupling system to study the nonlinear dynamic system's behavior. Model simulations show that autoregulation of E-C coupling contractility naturally arises from the MCET feedback, enabling the cardiomyocyte to autoregulate contractility in compensatory response to load changes. However, excessively high load causes SR Ca2+ overload, spontaneous Ca2+ release, and arrhythmogenic activities. These model predictions are verified by experimental data. In conclusion, our experimental and modeling studies reveal an Autoregulatory E-C coupling dynamic system in the cardiomyocytes contracting under mechanical load. Deciphering the autoregulatory E-C couplingdynamics and MCET mechanisms will be essential for understanding how the heart autoregulates contractility in compensatory response to physiological load changes to maintain cardiac output, and why pathological loading (i.e., hypertension, TAC pressure-overload) leads to arrhythmias and heart failure.