Ordinary Differential Equations and Applied Dynamics Commons^™

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

EWU Masters Thesis Collection

No abstract provided.

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 …

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, …

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 …

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 …

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 …

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 …

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.

Mathematical Modelling Of Disease Outbreak, Favour Christian, Matthew Molloy

SURE Journal: Science Undergraduate Research Experience Journal

Establishing a model framework for more research necessitates a thorough understanding of the causes, distribution, prevalence, and evolution of infectious illnesses. The main mathematical concept used in this modelling simulation is ordinary differential equations (ODEs). The purpose of this study was to investigate the significance of the many criteria linked to a zombie virus spread. The zombie framework provides an accessible and relatively simple representation of the nature of infectious disease spread, allowing for tractable assumptions and the development of more complex situations.

The models are designed around a zombie outbreak in which the zombie virus is spread through a …

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

The Journal of Purdue Undergraduate Research

No abstract provided.

(R2099) Boundedness And Square Integrability In Neutral Differential Equations With Delay And Exponential Stability In Nonlinear Differential Equations Of Third-Order, Fatima Abdellaoui, Mebrouk Rahmane

Applications and Applied Mathematics: An International Journal (AAM)

The Lyapunov second method is an eigenvalue-based technique which consist of finding a Lyapunov function candidate for studying the stability of dynamical systems which is hard to deal with especially in most of nonlinear cases. Studying the stability and some of other qualitative behaviors based on the Lyapunov second method is research topic of actuality because of the wide range of applications of the differential equations. Many authors in the literature have used the second method of Lyapunov in the study of some qualitative behaviors from which the stability, the boundedness and the square integrability of solutions for various kinds …

(R2090) Analysis Of Heat And Mass Transfer In Mhd Boundary Layer Flow Of Chemically Reacting Fluid, Dharati Sheth, Manisha Patel, Dilip Joshi

Applications and Applied Mathematics: An International Journal (AAM)

Analysis of the effects of heat and mass transfer on the chemically responding boundary layer flow of a Casson fluid across a porous stretched sheet in the existence of a crosswise magnetic field is the aim of the existing work. The partial differential equations that control the current flow problems can be converted into similarity equations by applying the right similarity technique. Our goal is to use the DTM-Pade approximation to analytically solve the derived similarity equations. The transformed similarity equations are a group of nonlinear ordinary differential equations for the present flow problem. The analytical approach of the differential …

(R2098) Dynamic Analysis Of Stochastic Leslie-Gower Biological Predator-Prey Model With Prey Cannibalism, Sada Nand Prasad, Itendra Kumar Universiry Of Delhi, India, Pawan Kumar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study the dynamical analysis of a stochastic Leslie–Gower biological predator– prey model. Earlier, the Leslie–Gower model was studied in the context of biological systems, including cases involving cannibalism. In our model, we investigate the dynamic properties of a stochastic Leslie–Gower predator–prey ecological system using the stability of invariant measures on invariant sets, where the invariant measures are shown to be ergodic. We also conduct a threshold analysis to study the stochastic persistence and extinction of species. Stochastic bifurcation is also examined. The theoretical results are supported by numerical simulations and examples. Intra-species competition is considered and …

(R2104) On The Qualitative Results Of Riemann-Liouville Fractional Order Nonlinear Neutral Singular Systems With Mixed Delays, Abdullah Yiğit, Cemil Tunç

Applications and Applied Mathematics: An International Journal (AAM)

In this manuscript, we discuss new conditions for asymptotic stability of nonlinear Riemann- Liouville fractional mixed-delay neutral singular systems. By constructing a set of improved Lyapunov-Krasovski˘ı functionals (LKFs), we establish some new delay-dependent conditions in terms of matrix inequality, which guarantees that the systems are asymptotically stable. In the particular case, we give four numerical examples with their solutions and graphs via MATLAB software demonstrating the practical applicability of these proven conditions. With this study, some conditions existing in the literature are developed and generalized.

A Dynamical Systems Approach For Modeling Malware Propagating Through A Network And Potential Solutions Towards Mitigating Spread, James Johnson

Cybersecurity Undergraduate Research Showcase

Many people draw close parallels between malware propagating through a network and an epidemic spreading through a population. Epidemics are often modeled by a Susceptible-Infected-Recovered (SIR) model, in which a similar system of equations can model the spread of a virus through a computer network, and can be simplified when making assumptions about the network itself and its fixed number of nodes and edges. In this instance, malware propagating in a network also should reflect the network it is propagating through, in which the dynamical system will factor in the nodes of the network and their properties. The system itself …

Leveraging Quantitative Systems Pharmacology For Dose Optimization In Oncology Drug Development, Blerta Shtylla

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Kreig: Gaining Insight Into Epidemics Through Use Of Mathematical Modeling, Christina Edholm

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Paradigm For Ecological Dynamics In Predator-Prey Systems: Applications To Climate Change, Grayson D. Adams, Aditi Ghosh Dr.

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modelling Saccharomyces Cerevisiae For The Production Of Fermented Beverages, Paul A. Valle Dr., Yolocuauhtli Salazar Dr., Luis N. Coria Dr., Oscar N. Soto Dr., Jesus B. Paez Dr.

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

From Ecology To Modeling Apps - Newts, Crayfish, And Slopes, Timothy Lucas

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.