Mathematical Model Of System Dynamics Research Articles

Analytical approach to solving the problems of nonlinear dynamics of systems with time-varying parameters under the conditions of the external environment reaction

Purpose. The development and application of analytical (including approximate) methods of analyzing nonlinear mathematical models of system dynamics, which have complex behavior due to the presence of time-dependent characteristics, is relevant for solving various classes of engineering problems. Therefore, the purpose of this work is mathematical modeling of problems of nonlinear dynamics of such systems, which allows determining the trajectory of the system's movement over time and other dynamic characteristics in accordance with their setting. Method. Based on the modern achievements of analytical, in particular asymptotic and numerical research methods based on existing software complexes, the possibility of non-local research and the formation of a sufficiently complete representation of the peculiarities of the behavior of nonlinear systems is considered. To achieve the goal, a mathematical model of the nonlinear dynamics of a system with time-varying properties is considered, provided that the reaction of the environment depends on the function of the speed of movement of the system to the n degree. The results. The solution of some engineering problems of the nonlinear dynamics of systems with time-varying characteristics of dependence for n=2 and systems whose response to the external environment can be a function of both whole and fractional degrees allow to determine the trajectory of the system's movement over time and other dynamic characteristics in accordance with before their production. Scientific novelty. The analytical dependence of the speed function of the dynamic process of the system with time-varying parameters was obtained for the nonlinearity parameter of the studied system most used in practice, n=2, for the reaction function of the external environment. Practical significance. The obtained analytical dependencies can be applied in a sufficiently wide range of research. Approximate analytical methods based on asymptotic approaches based on hybrid methods (perturbation, phase integrals in combination with Galerkin's principle) are applied. The use of asymptotic and numerical methods of research based on existing software complexes opens up the possibility of non-local research and the formation of a sufficiently complete representation of the peculiarities of the behavior of nonlinear systems with variable characteristics of materials, in particular, composite and functionally gradient ones.

A mathematical model for choosing an action plan for the prevention and elimination of flood effects

The article presents the development of a mathematical model of system dynamics to forecast the flood effects characteristics. The model is based on a causal diagram and is presented by a system of nonlinear differential equations. The solution results of the system of differential equations were compared to real data of the flood that occurred in Primorye in 2001.The results obtained from the model can be used when developing a new effective action plan for flood prevention and response or correcting the current action plan.The FCFAAD information system was developed, which allows calculating the flood effects characteristics and choosing an action plan for flood prevention and response.

Synthesis of the Algorithm for Control of the Thermal Power Plant Generating Equipment Based on System Dynamics Models

The article discusses an original solution for designing an algorithm for selecting the most optimal technical and economic indicators for the operation of generating equipment of thermal power plants, taking into account the requirements of the wholesale electricity market, the day-ahead market and the balancing market. To design an algorithm for controlling generating equipment, the activity of a generating company in the wholesale electricity market was considered in terms of system dynamics. The proposed solution made it possible to select and interpret the state variables of the model, build flow diagrams describing the functioning of a technical-economic system, and visualize cause-and-effect relationships in the form of structured functional dependencies. In this work according to the norms of industry legislation and previously conducted scientific research the most important parameters were identified that form the flows of a dynamic technical and economic system, which are optimization criteria in fact. On the basis of this data, a stream stratification of the production processes of generating companies was carried out and a complex of mathematical models of system dynamics was developed to determine and plan the financial efficiency of the operation of thermal power plants and generating companies. The mathematical apparatus and the algorithm of its functioning are developed on the basis of the digraph of cause-and-effect relationships between the investigated technical and economic indicators. On the basis of the graph of interrelationships of system variables, a system of nonlinear differential equations has been built, which makes it possible to determine planned performance indicators when various technical and economic conditions change. The novelty of the proposed approach is the use of new model solutions based on the mathematical apparatus of system dynamics to represent the proposed model in simulation systems, in industry ERP and MES systems, for the development of DDS.

Mathematical model of system dynamics for heat utilization from ventilation emissions with intermediate heat carrier as an object of automation

Annotation Purpose. Formulation of a mathematical description of the non-stationary thermal regime of the heat utilization system of ventilation emissions on the basis of a heat exchanger with an intermediate heat carrier for industrial premises. Methods. The specificity of the object under study determines the analytical method of research, which is based on the analysis of the thermal balance of the elements of the studied system and the heat and energy connections between them. Results. A mathematical description of the dynamics of the thermal process in a recuperative heat recovery unit with an intermediate heat carrier is formulated taking into account the variable parameters of ventilation air, both exhaust and supply air and the presence of condensation on the surface of the heat exchanger. Given the possibility of automatic control of the operation of the disposal system by changing the flow of intermediate coolant (which makes the system of equations nonlinear), a linearized mathematical model of the dynamics of the studied system is proposed. Conclusions 1. The obtained mathematical models allow to determine the dynamic characteristics of the system of waste heat utilization in transient modes, as well as to evaluate the efficiency of the system itself and to optimize the parameters of heat exchangers. 2. The linearized model of the thermal utilizer allows to synthesize the system of automatic control of the operating mode and to investigate its parameters. Keywords: waste heat utilization, heat exchanger recuperator, intermediate heat carrier, dynamic mode, mathematical model, production room.

Methodology for Increasing the Efficiency of Dynamic Process Calculations in Elastic Elements of Complex Engineering Constructions

This study deals with a methodology for increasing the efficiency of dynamic process calculations in elastic elements of complex engineering constructions. We studied the complex dynamic processes in a simple engineering construction, a mechanical system of an elastic body–continuous flow of homogeneous medium. The developed methodology is based on the use of a priori information on some of the vibrations forms, the construction of a “simplified” mathematical model of system dynamics, and the obtaining of an analytical relationship that describe the overall range of factors on the elastic vibrations of system. The methodology is used for cases of complex vibrations of elastic bodies, and the obtained results can serve as a basis for choosing the main technological and operational parameters of elastic elements of mechanisms and machines that perform complex vibrations. The results obtained in this work are the basis for calculating the blast effect on the elements of protective structures in order to increase their protective capacity by improving the method of their attachment or by using additional reinforcement, buff load effects on the elements of drilling strings and dynamic processes that occur during surface strengthening by work hardening in order to avoid resonance phenomena, and technological processes of vibration displacement or vibration separation of granular media.

About Mathematical Models of System Dynamics with Geometric Constraints in Problems of Stability and Stabilization by Incomplete State Information

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Mathematical Model of Innate and Adaptive Immunity of Sepsis: A Modeling and Simulation Study of Infectious Disease.

Sepsis is a systemic inflammatory response (SIR) to infection. In this work, a system dynamics mathematical model (SDMM) is examined to describe the basic components of SIR and sepsis progression. Both innate and adaptive immunities are included, and simulated results in silico have shown that adaptive immunity has significant impacts on the outcomes of sepsis progression. Further investigation has found that the intervention timing, intensity of anti-inflammatory cytokines, and initial pathogen load are highly predictive of outcomes of a sepsis episode. Sensitivity and stability analysis were carried out using bifurcation analysis to explore system stability with various initial and boundary conditions. The stability analysis suggested that the system could diverge at an unstable equilibrium after perturbations if r t2max (maximum release rate of Tumor Necrosis Factor- (TNF-) α by neutrophil) falls below a certain level. This finding conforms to clinical findings and existing literature regarding the lack of efficacy of anti-TNF antibody therapy.

Dynamic Study of 8-R Seven Bar III Degree of Freedom Linkage Mechanism

The system dynamics mathematical model for 8-R seven-bar Ⅲ linkage is induced through plurality, and then translated into matrix format, the modeling is solved for given mathematical model as well as the correctness of overcome is analyzed to give relative response curve, and the purpose is to calculate energetic parameter during the mechanism working precisely, meanwhile experiment results show constraint reaction force and driving force in the process of shearing with rolling-cutting bilateral shear , by using statistical energetic parameter to verify the correctness of above mentioned mathematical model as well , which gives a basis for design , control principle analysis and practical use for the mechanism .

Selection Mechanisms Underlying High Impact Biomedical Research - A Qualitative Analysis and Causal Model

BackgroundAlthough scientific innovation has been a long-standing topic of interest for historians, philosophers and cognitive scientists, few studies in biomedical research have examined from researchers' perspectives how high impact publications are developed and why they are consistently produced by a small group of researchers. Our objective was therefore to interview a group of researchers with a track record of high impact publications to explore what mechanism they believe contribute to the generation of high impact publications.Methodology/Principal FindingsResearchers were located in universities all over the globe and interviews were conducted by phone. All interviews were transcribed using standard qualitative methods. A Grounded Theory approach was used to code each transcript, later aggregating concept and categories into overarching explanation model. The model was then translated into a System Dynamics mathematical model to represent its structure and behavior. Five emerging themes were found in our study. First, researchers used heuristics or rules of thumb that came naturally to them. Second, these heuristics were reinforced by positive feedback from their peers and mentors. Third, good communication skills allowed researchers to provide feedback to their peers, thus closing a positive feedback loop. Fourth, researchers exhibited a number of psychological attributes such as curiosity or open-mindedness that constantly motivated them, even when faced with discouraging situations. Fifth, the system is dominated by randomness and serendipity and is far from a linear and predictable environment. Some researchers, however, took advantage of this randomness by incorporating mechanisms that would allow them to benefit from random findings. The aggregation of these themes into a policy model represented the overall expected behavior of publications and their impact achieved by high impact researchers.ConclusionsThe proposed selection mechanism provides insights that can be translated into research coaching programs as well as research policy models to optimize the introduction of high impact research at a broad scale among institutional and governmental agencies.

Dynamic causal models of neural system dynamics: current state and future extensions

Complex processes resulting from interaction of multiple elements can rarely be understood by analytical scientific approaches alone; additional, mathematical models of system dynamics are required. This insight, which disciplines like physics have embraced for a long time already, is gradually gaining importance in the study of cognitive processes by functional neuroimaging. In this field, causal mechanisms in neural systems are described in terms of effective connectivity. Recently, dynamic causal modelling (DCM) was introduced as a generic method to estimate effective connectivity from neuroimaging data in a Bayesian fashion. One of the key advantages of DCM over previous methods is that it distinguishes between neural state equations and modality-specific forward models that translate neural activity into a measured signal. Another strength is its natural relation to Bayesian model selection (BMS) procedures. In this article, we review the conceptual and mathematical basis of DCM and its implementation for functional magnetic resonance imaging data and event-related potentials. After introducing the application of BMS in the context of DCM, we conclude with an outlook to future extensions of DCM. These extensions are guided by the long-term goal of using dynamic system models for pharmacological and clinical applications, particularly with regard to synaptic plasticity.