Parameter Identification in Ecological Systems via Discontinuous and Singular Control Regimes

2012 ◽  
Author(s):  
Dale B. McDonald ◽  
Joseph O. Falade
Keyword(s):  
Mathematical Models ◽  
Dynamic Models ◽  
Singular Control ◽  
Single Species ◽  
Ecological Systems ◽  
Critical Parameters ◽  
Regulatory Agencies ◽  
Commercial Fishing ◽  
Policy Decisions ◽  
Simulation Results

Policy decisions regarding commercial harvesting of aquatic species by (typically governmental) regulatory agencies are often based in part upon field data, simulation results, and mathematical models. Regulatory agencies may limit or expand seasons, determine total harvest allowed, increase or decrease licensure fees, and raise or lower taxation rates in response to the state of the ecological system. Ultimately, the regulatory agency uses such measures to ensure viable populations in an attempt to balance ecosystem health and benefits for society. Such decisions impact commercial fishing ventures affecting the nature of harvesting efforts and their intensity. Conclusions drawn from mathematical models of ecological systems, and derived simulation results which affect this reality are highly dependent upon the validity of information available. Knowledge or estimates of critical parameters such as intrinsic growth rate, carrying capacity, etc. and dynamic variables such as biomass levels dictate the usefulness of analytical and numerical analyses. The purpose of this treatment is to illustrate that control laws applied to mathematical models of species dynamics may be used to discern estimates of parameters that inherently exist in such models in an effort to provide more valuable information upon which to base policy decisions. Dynamic models of both single-species evolution and predator-prey interactions are examined.

Fractal analysis and control of the competition model

2016 ◽  
Vol 09 (03) ◽  
pp. 1650045 ◽  
Author(s):  
Mianmian Zhang ◽  
Yongping Zhang
Keyword(s):  
Feedback Control ◽  
Mathematical Models ◽  
Fractal Analysis ◽  
Fractal Geometry ◽  
Julia Set ◽  
Julia Sets ◽  
Competition Model ◽  
Simulation Results ◽  
Population Competition ◽  
And Control

Lotka–Volterra population competition model plays an important role in mathematical models. In this paper, Julia set of the competition model is introduced by use of the ideas and methods of Julia set in fractal geometry. Then feedback control is taken on the Julia set of the model. And synchronization of two different Julia sets of the model with different parameters is discussed, which makes one Julia set change to be another. The simulation results show the efficacy of these methods.

A Detection and Warning System for Unintended Acceleration

2015 ◽  
Author(s):  
Hongtao Yu ◽  
Reza Langari
Keyword(s):  
Mathematical Models ◽  
Diagnostic System ◽  
Warning System ◽  
Diagnostic Algorithm ◽  
Data Driven ◽  
Simulation Results ◽  
Major Factors

This paper presents a data-driven method to detect vehicle problems related to unintended acceleration (UA). A diagnostic system is formulated by analyzing several specific vehicle events such as acceleration peaks and generating corresponding mathematical models. The diagnostic algorithm was implemented in the Simulink/dSpace environment for validation. Major factors that affect vehicles’ acceleration (e.g., changes of road grades and gear shifting) were included in the simulation. UA errors were added randomly when human drivers drove virtual cars. The simulation results show that the algorithm succeeds in detecting abnormal acceleration.

scholarly journals Development of a New Bead Movement-Based Computational Framework Shows that Bacterial Amyloid Curli Reduces Bead Mobility in Biofilms

2020 ◽  
Vol 202 (18) ◽  
Author(s):  
K. Malhotra ◽  
T. Hunter ◽  
B. Henry ◽  
Y. Ishmail ◽  
P. Gaddameedi ◽  
...  
Keyword(s):  
Mathematical Models ◽  
Open Source ◽  
Material Properties ◽  
Laser Scanning ◽  
Cell Movement ◽  
Laser Scanning Confocal Microscopy ◽  
Critical Parameters ◽  
Gastrointestinal Microbiota ◽  
Content Type ◽  
Scanning Confocal Microscopy

ABSTRACT Biofilms exist in complex environments, including the intestinal tract, as a part of the gastrointestinal microbiota. The interaction of planktonic bacteria with biofilms can be influenced by material properties of the biofilm. During previous confocal studies, we observed that amyloid curli-containing Salmonella enterica serotype Typhimurium and Escherichia coli biofilms appeared rigid. In these studies, Enterococcus faecalis, which lacks curli-like protein, showed more fluid movement. To better characterize the material properties of the biofilms, a four-dimensional (4D) model was designed to track the movement of 1-μm glyoxylate beads in 10- to 20-μm-thick biofilms over approximately 20 min using laser-scanning confocal microscopy. Software was developed to analyze the bead trajectories, the amount of time they could be followed (trajectory life span), the velocity of movement, the surface area covered (bounding boxes), and cellular density around each bead. Bead movement was found to be predominantly Brownian motion. Curli-containing biofilms had very little bead movement throughout the low- and high-density regions of the biofilm compared to E. faecalis and isogenic curli mutants. Curli-containing biofilms tended to have more stable bead interactions (longer trajectory life spans) than biofilms lacking curli. In biofilms lacking curli, neither the velocity of bead movement nor the bounding box volume was strictly dependent on cell density, suggesting that other material properties of the biofilms were influencing the movement of the beads and flexibility of the material. Taken together, these studies present a 4D method to analyze bead movement over time in a 3D biofilm and suggest curli confers rigidity to the extracellular matrix of biofilms. IMPORTANCE Mathematical models are necessary to understand how the material composition of biofilms can influence their physical properties. Here, we developed a 4D computational toolchain for the analysis of bead trajectories, which laid the groundwork for establishing critical parameters for mathematical models of particle movement in biofilms. Using this open-source trajectory analyzer, we determined that the presence of bacterial amyloid curli changes the material properties of a biofilm, making the biofilm matrix rigid. This software is a powerful tool to analyze treatment- and environment-induced changes in biofilm structure and cell movement in biofilms. The open-source analyzer is fully adaptable and extendable in a modular fashion using VRL-Studio to further enhance and extend its functions.

scholarly journals Predicting Collapse of Complex Ecological Systems: Quantifying the Stability-Complexity Continuum

2019 ◽  
Author(s):  
Susanne Pettersson ◽  
Van M. Savage ◽  
Martin Nilsson Jacobi
Keyword(s):  
Single Species ◽  
Ecological Systems ◽  
Ecological Research ◽  
Stability Criteria ◽  
Numerical Techniques ◽  
Intermediate Regime ◽  
Limits Of Stability ◽  
Species Abundances ◽  
The Stability ◽  
Degree Of Instability

Dynamical shifts between the extremes of stability and collapse are hallmarks of ecological systems. These shifts are limited by and change with biodiversity, complexity, and the topology and hierarchy of interactions. Most ecological research has focused on identifying conditions for a system to shift from stability to any degree of instability—species abundances do not return to exact same values after perturbation. Real ecosystems likely have a continuum of shifting between stability and collapse that depends on the specifics of how the interactions are structured, as well as the type and degree of disturbance due to environmental change. Here we map boundaries for the extremes of strict stability and collapse. In between these boundaries, we find an intermediate regime that consists of single-species extinctions, which we call the Extinction Continuum. We also develop a metric that locates the position of the system within the Extinction Continuum—thus quantifying proximity to stability or collapse—in terms of ecologically measurable quantities such as growth rates and interaction strengths. Furthermore, we provide analytical and numerical techniques for estimating our new metric. We show that our metric does an excellent job of capturing the system behaviour in comparison with other existing methods—such as May’s stability criteria or critical slowdown. Our metric should thus enable deeper insights about how to classify real systems in terms of their overall dynamics and their limits of stability and collapse.

scholarly journals Mathematical Models for Assessing Vaccination Scenarios in Several Provinces in Indonesia

2020 ◽  
Author(s):  
N. Nuraini ◽  
K. Khairudin ◽  
P. Hadisoemarto ◽  
H. Susanto ◽  
A. Hasan ◽  
...  
Keyword(s):  
Mathematical Models ◽  
Age Groups ◽  
Transmission Model ◽  
West Java ◽  
Dynamic Transmission Model ◽  
Simulation Results ◽  
Age Structured

AbstractTo mitigate more casualties from the COVID-19 outbreak, this study assessed optimal vaccination scenarios, considering some existing healthcare conditions and some assumptions, by developing SIQRD (Susceptible-Infected-Quarantine-Recovery-Death) models for Jakarta, West Java, and Banten, in Indonesia. The models included an age-structured dynamic transmission model that naturally could give different treatments among age groups of population. The simulation results show that the timing and period’s length of the vaccination should be well planned and prioritizing particular age groups will give significant impact on the total number of casualties.

Mathematical Models for Model-Based Control in Offshore Pipelay Operations

2009 ◽  
Author(s):  
Gullik A. Jensen ◽  
Thor I. Fossen
Keyword(s):  
Mathematical Models ◽  
Dynamic Models ◽  
Controller Design ◽  
Computational Time ◽  
Beam Model ◽  
Time Dynamic ◽  
Model Based ◽  
On Line ◽  
Stability And Accuracy ◽  
Control Application

This paper considers mathematical models for model-based controller design in offshore pipelay operations. Three classes of models for control design are discussed, real-world models suitable for controller design verification, controller and observer models which are used on-line in the control system implementation. The control application place requirements on the model with respect to the computational time, dynamic behavior, stability and accuracy. Models such as the beam model, two catenary models, as well as general finite element (FE) models obtained from computer programs were not able to meet all of the requirements, and two recent dynamic models designed for control are presented, which bridge the gap between the simple analytical and more complex FE models. For completeness, modeling of the pipelay vessel, stinger and roller interaction, soil and seabed interaction and environmental loads are discussed.

Numerical analysis of hemivariational inequalities in contact mechanics

Acta Numerica ◽  
2019 ◽  
Vol 28 ◽  
pp. 175-286 ◽  
Author(s):  
Weimin Han ◽  
Mircea Sofonea
Keyword(s):  
Numerical Analysis ◽  
Mathematical Models ◽  
Contact Mechanics ◽  
Numerical Solutions ◽  
Deformable Body ◽  
Industrial Process ◽  
Contact Problems ◽  
Hemivariational Inequalities ◽  
Uniqueness Results ◽  
Simulation Results

Contact phenomena arise in a variety of industrial process and engineering applications. For this reason, contact mechanics has attracted substantial attention from research communities. Mathematical problems from contact mechanics have been studied extensively for over half a century. Effort was initially focused on variational inequality formulations, and in the past ten years considerable effort has been devoted to contact problems in the form of hemivariational inequalities. This article surveys recent development in studies of hemivariational inequalities arising in contact mechanics. We focus on contact problems with elastic and viscoelastic materials, in the framework of linearized strain theory, with a particular emphasis on their numerical analysis. We begin by introducing three representative mathematical models which describe the contact between a deformable body in contact with a foundation, in static, history-dependent and dynamic cases. In weak formulations, the models we consider lead to various forms of hemivariational inequalities in which the unknown is either the displacement or the velocity field. Based on these examples, we introduce and study three abstract hemivariational inequalities for which we present existence and uniqueness results, together with convergence analysis and error estimates for numerical solutions. The results on the abstract hemivariational inequalities are general and can be applied to the study of a variety of problems in contact mechanics; in particular, they are applied to the three representative mathematical models. We present numerical simulation results giving numerical evidence on the theoretically predicted optimal convergence order; we also provide mechanical interpretations of simulation results.

scholarly journals Predicting collapse of complex ecological systems: quantifying the stability–complexity continuum

2020 ◽  
Vol 17 (166) ◽  
pp. 20190391 ◽  
Author(s):  
Susanne Pettersson ◽  
Van M. Savage ◽  
Martin Nilsson Jacobi
Keyword(s):  
Single Species ◽  
Ecological Systems ◽  
Ecological Research ◽  
Stability Criteria ◽  
Numerical Techniques ◽  
Intermediate Regime ◽  
Limits Of Stability ◽  
Species Abundances ◽  
The Stability ◽  
Degree Of Instability

Dynamical shifts between the extremes of stability and collapse are hallmarks of ecological systems. These shifts are limited by and change with biodiversity, complexity, and the topology and hierarchy of interactions. Most ecological research has focused on identifying conditions for a system to shift from stability to any degree of instability—species abundances do not return to exact same values after perturbation. Real ecosystems likely have a continuum of shifting between stability and collapse that depends on the specifics of how the interactions are structured, as well as the type and degree of disturbance due to environmental change. Here we map boundaries for the extremes of strict stability and collapse. In between these boundaries, we find an intermediate regime that consists of single-species extinctions, which we call the extinction continuum. We also develop a metric that locates the position of the system within the extinction continuum—thus quantifying proximity to stability or collapse—in terms of ecologically measurable quantities such as growth rates and interaction strengths. Furthermore, we provide analytical and numerical techniques for estimating our new metric. We show that our metric does an excellent job of capturing the system's behaviour in comparison with other existing methods—such as May’s stability criteria or critical slowdown. Our metric should thus enable deeper insights about how to classify real systems in terms of their overall dynamics and their limits of stability and collapse.

scholarly journals Nonlinear inversion method based on dynamics model modification

2019 ◽  
Vol 288 ◽  
pp. 01003
Author(s):  
Faping Zhang ◽  
Kai Wu
Keyword(s):  
Dynamic Models ◽  
Error Function ◽  
Experimental Results ◽  
Inversion Method ◽  
Nonlinear Inversion ◽  
Forward Modelling ◽  
Dynamics Model ◽  
Model Modification ◽  
Simulation Results ◽  
The Cost

In the fields of modern aviation system, subgrade vehicle system and complex mechanical system, there is a problem that parameters of most dynamic models are inaccurate. This problem results in a large difference between the model results and the experimental results. In order to solve this problem, this paper build a nonlinear inversion method based on dynamics model modification (NIDM). Firstly, the error relationship was obtained by integrating the experimental data with the simulation results of the forward modelling model by the cost function and penalty function. Then, the problem of error function minimization was solved by using the parameter iteration generated by particle swarm optimization algorithm, and the corrected parameters of the forward modelling model were obtained. Finally, the method was tested by building a vehicle suspension vibration model and a pavement excitation model as test samples. The test results show that the fitting degree between the simulation results and the experimental results can be effectively improved by modifying the parameters of the dynamic model based on the NIDM method.

scholarly journals Modelling ecological systems in a changing world

2012 ◽  
Vol 367 (1586) ◽  
pp. 181-190 ◽  
Author(s):  
Matthew R. Evans
Keyword(s):  
Environmental Change ◽  
Mathematical Models ◽  
Ecological Systems ◽  
Ecological Modelling ◽  
Causal Relationships ◽  
Future State ◽  
The World ◽  
The Future ◽  
The Impact ◽  
The Way

The world is changing at an unprecedented rate. In such a situation, we need to understand the nature of the change and to make predictions about the way in which it might affect systems of interest; often we may also wish to understand what might be done to mitigate the predicted effects. In ecology, we usually make such predictions (or forecasts) by making use of mathematical models that describe the system and projecting them into the future, under changed conditions. Approaches emphasizing the desirability of simple models with analytical tractability and those that use assumed causal relationships derived statistically from data currently dominate ecological modelling. Although such models are excellent at describing the way in which a system has behaved, they are poor at predicting its future state, especially in novel conditions. In order to address questions about the impact of environmental change, and to understand what, if any, action might be taken to ameliorate it, ecologists need to develop the ability to project models into novel, future conditions. This will require the development of models based on understanding the processes that result in a system behaving the way it does, rather than relying on a description of the system, as a whole, remaining valid indefinitely.

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