Dynamic Systems Commons^™

Using Mathematical Modeling To Study The Dynamics Of Legionnaires’ Disease And Consider Management Options, Mark Z. Wang, Christina J. Edholm, Lihong Zhao

Faculty Articles

Legionnaires' disease (LD) is a largely understudied and underreported pneumonic environmentally transmitted disease caused by the bacteria \textit{Legionella}. It primarily occurs in places with poorly maintained artificial sources of water. There is currently a lack of mathematical models on the dynamics of LD. In this paper, we formulate a novel ordinary differential equation-based susceptible-exposed-infected-recovered (SEIR) model for LD. One issue with LD is the difficulty in its detection, as the majority of countries around the world lack the proper surveillance and diagnosis methods. Thus, there is not much publicly available data or literature on LD. We use parameter estimation for …

Dual Quaternions For Gravity Recovery Missions, Ryan Kinzie

Doctoral Dissertations and Master's Theses

A dual quaternion-based modeling, state estimation and control approach is introduced as a better alternative to the traditional methods which are currently utilized for gravity recovery missions. The proposed modeling and control approach was verified against and compared to the tangent bundle to Special Euclidean Group 3 through MATLAB simulations. The dual quaternion-based approach shows superior performance over traditional linearized and uncoupled methodologies, in both modeling accuracy of spacecraft translational position, and the ability to control the pose of a test mass relative to its host spacecraft. Utilizing data products from the Gravity Recovery and Climate Experiment Follow-On mission, a …

Analysis Of Systematic Trade-Offs Between Military And Healthcare Expenditure Alongside Gdp Growth Of Select Asian And Western Exporting Economies In The 21st Century, Rahul Balamurugan, Carlos Gershenson, Preethi Nanjundan, Hiroki Sayama

Northeast Journal of Complex Systems (NEJCS)

This study explores the complexity in the trade-offs between military expenditure, healthcare expenditure, and GDP growth across select Asian nations and major weapon-exporting countries, examining how nations allocate finite resources between national security and human well-being over the past two decades. Using a systems science approach, the research integrates Granger causality testing to analyze temporal and directional relationships among GDP growth, military expenditure, and healthcare expenditure, uncovering their dynamic interdependencies. The methodology includes trend and slope analysis, Granger causality testing, outlier detection, and clustering to identify heterogeneity in resource allocation strategies. Developed, weapon-exporting nations exhibit complementary trends, with strong causality …

Integrating Neural Networks For Predictive Torque Control And Obstacle Avoidance In Autonomous Robot, Viswanath Kodali, Harsha Vardhan Borra, Kiran P

Northeast Journal of Complex Systems (NEJCS)

In the field of robotics, precise motion control and accurate computation of joint forces are critical for ensuring optimal performance. Traditional methods, such as using the Jacobian matrix for joint angle determination and Euler-Lagrange equations for torque computation, are reliable but computationally intensive, making them less suitable for real-time applications. This paper presents an advanced approach to improving the productivity and efficiency of a 3-Degree of Freedom (DOF) robotic arm by utilizing Artificial Neural Network (ANN). The proposed system dynamically predicts joint angles and torque, enabling faster and more efficient motion control.

To address the challenge of obstacle avoidance in …

Finite Hybrid- And Semi-Markov Chains, Jose L. Menaldi, Maurice Robin

Mathematics Faculty Research Publications

The ergodic behaviour of finite Markov chains having also instantaneous transition are considered. Some estimates are obtained which complement our previous work [29]. Also, an optimal switching control model for semi-Markov chains is analysed, without any particular assumptions on the recurrent classes.

The Presence Of Outer Giant Planets And Their Role In Inner Planet Formation With And Without Their Influence, Mateo E. Guerra Toro

Graduate Theses/Dissertations

We performed dynamical simulations of the giant impact phase of planet formation to investigate the formation of inner terrestrial planets under the influence of 4 solar system-like outer giant planets. We developed a new code using the N-body simulation suite REBOUND and REBOUNDx (Rein et al. (2019) and Tamayo et al. (2019)) to simulate 2 stages of planetary formation: a residual gaseous protoplanetary disk phase and subsequent dynamical evolution after the disk photoevaporates. The initial conditions for the inner planetary embryos were taken by Morrison et al. (2020) based on a range of solid surface densities that produced Super-Earth terrestrial …

Modeling The Impacts Of The Current And Projected Temperatures On Spongy Moth Population Dynamics, Adrienne B. Spring

Theses and Dissertations

The spongy moth (Lymantria dispar) is an invasive forest pest that has caused significant ecological damage across the United States. Its invasion front is shaped by a number of factors, including temperature in both the northern and southern regions. With ongoing climate change, areas that were previously uninhabitable may become increasingly favorable for moth population establishment and expansion, while other areas may experience thermal stress limiting persistence. This study develops a temperature-driven population model to analyze how temperature affects the spongy moth population dynamics along the invasion front. This model incorporates temperature effects on fecundity, stage-specific survival rates, …

Wave Reflections In A Biophysically Detailed Model Of Cardiac Tissue, Grace Moberg

Honors Theses

Regular heart rhythms are governed by the coordinated spread of action potentials through cardiac tissue. The interaction of an action potential with a tissue heterogeneity may lead to a reflection, where both a retrograde and an anterograde wave propagate off of the initial impulse. Reflections have been experimentally linked to cardiac arrhythmias, but their mechanisms of generation are not well-understood. Mathematically, reflections in phenomenological models of cardiac tissue have been linked to an unstable periodic orbit. These models typically sacrifice detail about the variety of ionic currents and processes involved in action potential propagation in favor of mathematical simplicity. Biophysically …

Dynamics Of Prey-Prey Mutualism With Varying Carrying Capacity And Herd Behavior In The Presence Of Predator, Felix Dela Djokoto

UNF Graduate Theses and Dissertations

This study investigates the dynamics of mutualistic relationships between two prey species in the presence of a predator, by taking into account herding in one species along with the influence of carrying capacities between two prey species. These mutualistic dynamics are presented by constructing two mathematical models, namely an indirect and direct mutualism model. As the strength of the symbiotic relationship increases the indirect model goes through transcritical bifurcation to Hopf bifurcation whereas in the direct mutualism model goes through saddle-node bifurcation to Hopf bifurcation.

Bound Preserving Discontinuous Galerkin Methods For Euler Equations And Nonequilibrium Flows, Fangyao Zhu

Dissertations, Master's Theses and Master's Reports

This dissertation is composed of four chapters in which we will closely examine the high order bound preserving discontinuous Galerkin methods for solving partial differential equations, specifically non-equilibrium chemical reacting flows and Euler equations under gravitational fields. A shared requirement between the two is the necessity for positive values of both density and pressure. Due to this physical nature of the two systems, constructing a positivity preserving scheme become very essential in our research.

For non-equilibrium flows where multi-reactions and multi-species are involved, we are also required to keep the bounds of the mass fraction of each species in between …

Mathematical Modeling Of Lead Climbing Falls, Rosemary Christmas Evans

EWU Masters Thesis Collection

This thesis presents a force-based mathematical model for simulating dynamic falls in lead sport climbing, with an emphasis on physical realism and empirical validation. The system is modeled as a mass–spring–damper, incorporating gravity, nonlinear rope stiffness, internal damping, and Capstan-style friction at protection points. The goal is to predict peak forces and rope elongation while capturing the complex dynamics of real climbing ropes. Several novel features are introduced. Activation switches ensure forces only engage when the rope is tensioned, preventing premature response. A velocity-sensitive stiffness transition function allows the rope to stiffen smoothly with increasing fall speed, reflecting rate-dependent rope …

Quantized Average Agreement Algorithms With Error Correction For Digraphs, Shuaib A. Mughal

Honors Undergraduate Theses

Multi-agent systems have become more and more prevalent as technology increasingly gets integrated into our daily lives. Some of these technological systems are large in size; for example, the smart grid where multiple devices are used to monitor and control different aspects of the energy grid. Another example is a team of autonomous systems deployed for a specific task. When these systems are spatially distributed, an important component of distributed algorithms is the ability for the agents to reach consensus on the global state of the system. Reaching agreement enables the spatially distributed agent make decisions or determine the next …

Mathematical Contributions To The Study Of Chemotaxis And Cell Signaling, Hajr Zam

Graduate Theses, Dissertations, and Problem Reports (ETD)

This dissertation presents results from two mathematical projects concerned with the biology of cells. Chapter 1 provides biological background and places the two mathematical problems in the context of cell signaling. The larger project, with Prof. H. Hattori on a chemotaxis model is presented in Chapters 3 and 4. Work with Prof. \'{A}. Hal\'{a}sz on a chemical reaction network system with linear multimers and two types of labels is presented in Chapter 2. The chemotaxis system describes the one-dimensional dynamics of a species of cells with two chemical species, a chemo-attractant and chemo-repellent. The goal is to analyze the behavior …

Essays On Technological Change And Scientific Research, Max Mayca

Electronic Theses & Dissertations (2024 - present)

The primary objective of economic science has long been to understand and promote growth, as it contributes to a more prosperous civilization and improves individual well-being. The core drivers of growth—capital accumulation, human capital development, and technological progress—are well-established. While capital deepening enables scaling of production, and human capital enhances labor productivity, technological and scientific advancements remain the most critical, as they continually redefine the efficiency frontier. Given this centrality, it is essential to understand how technological progress affects labor markets, how research resources should be allocated, and how technology relates to human capital formation.

The first part of this …

Safety And Optimality Monitors For Learning-Enabled Systems Using Conformal Prediction, Jackson Cox

McKelvey School of Engineering Graduate Student Theses & Dissertations

The use of machine learning to create data-driven plant models and controllers has led to an increased need for safety and optimality monitors for model-based systems. System plant models are subject to uncertainty due to learning constraints such as unseen data and overfitting or physical constraints such as unknown dynamics and noise. This uncertainty is detrimental to safety-critical systems and must be properly regulated. To curb this uncertainty, we create prediction sets using the guarantees provided by Conformal Prediction. With a user-specified high probability, these prediction sets contain the true plant system states for an entire prediction horizon, which we …

The Mathematical Laws Of Morphology And Biomechanics Through Ontogeny, Wijesooriya Kisal Wijesooriya

The Journal of Purdue Undergraduate Research

No abstract provided.

Theory And Algorithms To Learn, Propagate, And Exploit Uncertainty For Stochastic Optimal Control Of Dynamical Systems, Vignesh Sivaramakrishnan

Electrical and Computer Engineering ETDs

Non-Gaussian uncertainty frequently arises in learning and control problems involving stochastic dynamical systems, particularly in autonomous vehicles, UAVs, satellites, and robotics. In this dissertation, we propose a new framework that leverages characteristic functions that provides a frequency-domain representation of random variables. The dissertation is structured into three key areas. First, we address model-based stochastic optimal control for linear systems with non-Gaussian noise, demonstrating that characteristic functions can be used to enforce chance constraints and control systems toward desired distributions. Second, we explore data-driven stochastic control, utilizing empirical characteristic functions to handle systems with unknown disturbances. In addition, we derive several …

(R2108) Global Asymptotic Stability Analysis Of Discrete Time Population Model With Allee Effect Through Lyapunov Function, Govind Jha, Neeraj Kumar, Sarita Jha

Applications and Applied Mathematics: An International Journal (AAM)

This study explores the idea of stability analysis by using Lyapunov functions in discrete time population models; this work focuses on the nth generation. Further, this investigation aims to extend global stability concepts to discrete-time models and considers the influence of the Allee effect on population dynamics. Mathematical formulations and specific modelling approaches are utilized to investigate the behavior of the population system. The results reveal a larger range of stability in comparison to previous findings, emphasizing the effectiveness of the Lyapunov function approach. Specifically highlighted here are the extension of global stability concepts to the nth generation providing insights …

Hitch Cart “Landing Gear”, Rebekah White, Jose Raygoza, Randy Hernandez, Brandon Leon

Mechanical Engineering

This report aims to allow our sponsor, to review our design process of the Hitch Cart Landing Gear Prototype. In the design overview section of this report, we discuss the primary design modifications we made to the wheel mechanism of the existing hitch cart prototype, including the addition of the ACME screws and the folding brackets. This allows our sponsor to see the intended improvements made to the past prototype and understand the primary goal of our project. Then, in the implementation section, we cover the entire manufacturing process to allow our sponsor to understand what manufacturing steps must be …

(R2102) Chaos Measure In A Discrete Sir Epidemic Model With Constant Recovery, Sonia Aneja, Itendra Kumar, Sada Nand Prasad

Applications and Applied Mathematics: An International Journal (AAM)

A discrete SIR epidemic model with constant recovery and bilinear incidence rate is investigated for emergence of regular and chaotic behaviour in the context of non linear dynamics and different viable settings. The Euler’s discretization method is employed to transform the continuous epidemic model into discrete model which has been used as the study model. Attention is paid to various bifurcation plots obtained by varying certain system parameters while keeping other parameters constant. Bifurcations indicate regular evolution followed by chaos. Regular and chaotic attractors have been drawn in the process. As part of chaos measure, numerical studies are extended to …