Ordinary Differential Equations and Applied Dynamics Commons^™

Stability Criteria For The Generalized El Borhamy-Rashad-Sobhy Equation, Mohamed El-Borhamy Assoc.Prof, Essam Eddin Rashad Prof., Fathi Mousa Dr., Mai Hamouda

Journal of Engineering Research

This article is concerned with the study of stability criteria for one of the generalization form of El Borhamy-Rashad Sobhy equation, which is a linear second-order ordinary differential equation with periodically time varying coefficients. Many engineering applications can be represented by this generalization, for instance, including the modeling of RLC circuit with time varying inductance, resistance and capacitance, and the vibration of a stretched string, whose mass per unit length is periodic, under a periodic motion. An approximate solution is derived by using the Wenhl-Kramers-Brillonin (WKB) approach. A method of constructing Liapunov function is employed to derive extra conditions for …

My Gai Study Partner For Odes, Milena C. Cuellar

Open Educational Resources

My GAI Study Partner for ODEs is a scaffolded sequence of learning activities designed to support students in an Ordinary Differential Equations (ODEs) course by integrating the use of Generative AI tools—specifically Copilot, a platform accessible to all CUNY students and faculty. The activities are rooted in experiential learning, flipped classroom strategies, and self-directed learning principles. The sequence begins with two preparatory activities that introduce students to the ethical use and foundational concepts of Generative AI, fostering digital literacy and critical reflection. These are followed by a series of main activities—initially structured (Activity 3) and later more flexible …

Exploration Of Differential Equation Models For Phage-Bacteria Population Dynamics, John Lawrence Palacios, Rebecca A. Segal

Spora: A Journal of Biomathematics

Bacteriophages are viruses that infect and replicate within bacteria. Lytic phages cause the bacterial cell to burst, killing the bacteria. These types of phages can be used to treat patients with antibiotic-resistant bacterial infections. As a step in developing successful treatment protocols, we aim to understand the population dynamics of phages and bacteria using an in vitro model. We model the dynamics using the Campbell model, which consist of a delay differential equation (DDE), as a base model. We extended the model by including the emergence of phage resistance. We then compared the DDE model with a parallel ordinary differential …

Modeling Covid-19 Spread And Effects Of Non-Pharmaceutical Interventions On A College Campus, Jakob Kotas, Priscilla Perey Ratonel

CODEE Journal

We consider an extension to the classical SIR compartmental model from mathematical epidemiology as applied to the spread of COVID-19 on a college campus. While the classical SIR model does not allow for recovered individuals to lose immunity, we alter the equations to allow for such (due to the rise of new variants), leading to a SIRS-type model. We study the system of ODEs analytically and through numerical simulation. Finally we discuss a quantitative approach for how college administrators can decide when to implement stricter non-pharmaceutical interventions (social distancing, mask mandates, quarantine, etc.) to eradicate the infection from the campus …

Quantitative Preventive Approaches To Diabetes: Mathematical Modeling And Analysis, Rushi P. Bhatt

Theses, Dissertations and Culminating Projects

The rising prevalence of diabetes presents a pressing global health concern, necessitating effective control strategies. This study aims to construct a mathematical model to analyze the influence of diverse factors on blood sugar levels, with a focus on identifying optimal methods for maintaining healthy glucose levels. Employing ordinary differential equations (ODE), the model investigates variables including leptin resistance, fat mass, glucose, insulin resistance, beta cell mass, daily physical activity, and dietary intake. Utilizing parameter estimates from existing literature, the model’s framework is established, and simulation results elucidate the intricate interplay between lifestyle choices and blood glucose dynamics. Furthermore, the model …

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 …

Horizontal Infiltration Of Water Through Porous Snow As A Gravity Current, Anthony Cheng

Dartmouth College Master’s Theses

On the surface of the Greenland ice sheet or around the margins of the Antarctic ice shelf, water infiltrates porous ice. It is important to understand this infiltration process since water populating the pore space of ice directly impacts the density, porosity, and wetness of ice. These properties influence the mechanics and tensile strength of ice, as greater amounts of infiltration result in faster or more widespread deformation events, which may lead to adverse climatic effects such as sea level rise and ocean current disruption. While studies have considered the thermodynamics and fluid mechanics of water vertically percolating through snow …

A Mathematical Modeling Approach To Investigate The Impacts Of Post-Infection Mortality And Partial Immunity On Disease Endemicity, Brendan M. Shrader

Honors Undergraduate Theses

A number of infectious diseases cause post-infection conditions or complications, such as COVID- 19, Q fever, and Polio. These conditions result in recovered individuals having a higher mortality rate than susceptibles, and this can impact disease dynamics. An existing mass-action model in the literature that incorporated post-infection mortality was shown to have limit cycles, or persistent oscillations, in the infected population. To better understand what causes these limit cycles, we develop and analyze a new epidemiological model with standard incidence. We show standard results, including the existence, uniqueness, and stability of the disease-free and endemic equilibria, and we rule out …

Scalable Parallel-In-Time Integration For Equations Of Motion, Nathan W. Chapman

All Master's Theses

Physical simulations always need to balance accuracy and run-time. This work implements the Parareal Algorithm using graphics processing units across a distributed system to accurately simulate time-dependent physics while attempting to minimize runtime. Data-transfer latency is identified as the primary bottleneck, for which mitigation methods are provided. Benchmarks comparing single-GPU and distributed implementations on a spectrum of coarse and fine discretizations are analyzed.

The Inverse Scattering Transform For The Nonlinear Schrödinger Equation, Ivan Casas-Rocha

Honors Undergraduate Theses

The Nonlinear Schrödinger (NLS) Equation, iψ_t + 1/2 ψ_xx ± |ψ|²ψ = 0, is a nonlinear partial differential equation which is used to model several physical phenomena including nonlinear effects inside optical fibers and the formation of rogue waves in shallow water. It is particu- larly difficult to study solutions to this equation due to the nonlinearity, and the nonlinearity leads to incredibly interesting solutions not found in linear PDEs such as solitons. In this thesis, we highlight two methods of obtaining solutions to the (NLS) equation: the Inverse Scattering Transform and the Dressing Method. Furthermore, …

Wildfire Modeling Using Systems Of Odes And Pdes, Michael A. Quindlen

EWU Masters Thesis Collection

No abstract provided.

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.

A Mathematical Model On The Temporal Dynamics Of Aviation Competitive Pricing, Tichaona Chikore,, Farai Nyabadza,

Journal of Aviation/Aerospace Education & Research

This study investigates the competitive dynamics of airport pricing using U.S. airport data to validate the findings. It employs linear and nonlinear ordinary differential equation models to analyze the influence of competitive interactions and internal factors on pricing decisions. The methodology involves parameter estimation via optimization techniques and quantile regression to capture heterogeneity across market segments. Mathematical analysis and simulation results show that if competitive coupling coefficients are low then there is weak competitive influence on pricing, with airports’ pricing largely driven by internal factors. Also, if the adjustment rates exhibit consistency across airports then internal dynamics are dominant in …

Time-Marching Quantum Algorithm For Simulation Of Nonlinear Lorenz Dynamics, Efstratios Koukoutsis, George Vahala, Min Soe, Kyriakos Hizanidis, Linda Vahala, Abhay K. Ram

Electrical & Computer Engineering Faculty Publications

Simulating nonlinear classical dynamics on a quantum computer is an inherently challenging task due to the linear operator formulation of quantum mechanics. In this work, we provide a systematic approach to alleviate this difficulty by developing an explicit quantum algorithm that implements the time evolution of a second-order time-discretized version of the Lorenz model. The Lorenz model is a celebrated system of nonlinear ordinary differential equations that has been extensively studied in the contexts of climate science, fluid dynamics, and chaos theory. Our algorithm possesses a recursive structure and requires only a linear number of copies of the initial state …

Weakly Reversible Deficiency Zero Realizations Of Polynomial Dynamical Systems, Neal Ryan Buxton

Graduate Theses, Dissertations, and Problem Reports (ETD)

Weakly reversible, deficiency zero (WR0) systems form a large class of polynomial ODEs modeling chemical reaction networks. Their behavior is exceptionally stable: they have unique positive steady states, which are locally asymptotically stable (they are also conjectured to be globally asymptotically stable). This powerful result (the Deficiency Zero Theorem) applies to a large class of high dimensional, nonlinear polynomial dynamics, and is independent of the choice of parameters in the model. In this dissertation we present two algorithms that expands the scope of the Deficiency Zero Theorem to:

1. Networks with WR0 realizations, i.e. networks that are not necessarily WR0 …

Individual And Collective Properties Of Tunable Photochemical Belousov-Zhabotinsky Micro-Reactors, Kudakwashe Benedict Shumba

Graduate Theses, Dissertations, and Problem Reports (ETD)

Cell-like model chemical systems are powerful tools that can be used to explore the role of intercellular coupling on population level behaviors in communities of biological cells. Firstly, we present a new method for fabricating such micro-reactors using the photosensitive Belousov–Zhabotinsky (BZ) reaction system employed in silica microparticles. These BZ micro-reactors have a tunable response to photochemical coupling, varying from a fully excitatory response to a fully inhibitory response. Their response can be tuned through variations in either the reactive mixture or, on an individual micro-reactor level, by changes in the synthesis temperature used during the fabrication of the silica …