Ordinary Differential Equations and Applied Dynamics Commons^™

Block And Weddle Methods For Solving Nth Order Linear Retarded Volterra Integro-Differential Equations, Raghad Kadhim Salih

Emirates Journal for Engineering Research

A proposed method is presented to solve n^th order linear retarded Volterra integro-differential equations (RVIDE's) numerically by using fourth-order block and Weddle methods. Comparison between numerical and exact results has been given in numerical examples for conciliated the accuracy of the results of the proposed scheme.

Using Differential Equations To Model Predator-Prey Relations As Part Of Scudem Modeling Challenge, Zachary Fralish, Bernard Tyson Iii, Anthony Stefan

Rose-Hulman Undergraduate Mathematics Journal

Differential equation modeling challenges provide students with an opportunity to improve their mathematical capabilities, critical thinking skills, and communication abilities through researching and presenting on a differential equations model. This article functions to display an archetype summary of an undergraduate student team’s response to a provided prompt. Specifically, the provided mathematical model estimates how certain stimuli from a predator are accumulated to trigger a neural response in a prey. Furthermore, it tracks the propagation of the resultant action potential and the physical flight of the prey from the predator through the analysis of larval zebrafish as a model organism. This …

Modeling Gene Expression With Differential Equations, Madison Kuduk

Capstone Showcase

Gene expression is the process by which the information stored in DNA is convertedinto a functional gene product, such as protein. The two main functions that makeup the process of gene expression are transcription and translation. Transcriptionand translation are controlled by the number of mRNA and protein in the cell. Geneexpression can be represented as a system of first order differential equations for the rateof change of mRNA and proteins. These equations involve transcription, translation,degradation and feedback loops. In this paper, I investigate a system of first orderdifferential equations to model gene expression proposed by Hunt, Laplace, Miller andPham in …

Exploration And Implementation Of Neural Ordinary Differential Equations, Long Huu Nguyen, Andy Malinsky

Capstone Showcase

Neural ordinary differential equations (ODEs) have recently emerged as a novel ap- proach to deep learning, leveraging the knowledge of two previously separate domains, neural networks and differential equations. In this paper, we first examine the back- ground and lay the foundation for traditional artificial neural networks. We then present neural ODEs from a rigorous mathematical perspective, and explore their advantages and trade-offs compared to traditional neural nets.

The Analysis Of Neural Heterogeneity Through Mathematical And Statistical Methods, Kyle Wendling

Theses and Dissertations

Diversity of intrinsic neural attributes and network connections is known to exist in many areas of the brain and is thought to significantly affect neural coding. Recent theoretical and experimental work has argued that in uncoupled networks, coding is most accurate at intermediate levels of heterogeneity. I explore this phenomenon through two distinct approaches: a theoretical mathematical modeling approach and a data-driven statistical modeling approach.

Through the mathematical approach, I examine firing rate heterogeneity in a feedforward network of stochastic neural oscillators utilizing a high-dimensional model. The firing rate heterogeneity stems from two sources: intrinsic (different individual cells) and network …

On A Hybrid Technique To Handle Analytical And Approximate Solutions Of Linear And Nonlinear Fractional Order Partial Differential Equations, Kamal Shah, Hammad Khalil, Ahmet Yildirim

Applications and Applied Mathematics: An International Journal (AAM)

This manuscript is devoted to consider Natural transform (NT) coupled with homotopy perturbation method (HPM) for obtaining series solutions to some linear and nonlinear fractional partial differential equations (FPDEs). By means of NT, we obtain the transformed problem which is then solved by using HPM. By means of Stehfest’s numerical algorithm and using the dual relationship of NT and Laplace transform, we calculate inverse NT for approximate solutions. The series solutions we obtain using the proposed method are in close agreement with the exact solutions. We apply the proposed method to some interesting problems to illustrate our main results.

Bifurcation Analysis For Prey-Predator Model With Holling Type Iii Functional Response Incorporating Prey Refuge, Lazaar Oussama, Mustapha Serhani

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we carried out the bifurcation analysis for a Lotka-Volterra prey-predator model with Holling type III functional response incorporating prey refuge protecting a constant proportion of the preys. We study the local bifurcation considering the refuge constant as a parameter. From the center manifold equation, we establish a transcritical bifurcation for the boundary equilibrium. In addition, we prove the occurrence of Hopf bifurcation for the homogeneous equilibrium. Moreover, we give the radius and period of the unique limit cycle for our system

On The Weighted Pseudo Almost Periodic Solutions Of Nicholson’S Blowflies Equation, Ramazan Yazgan, Cemil Tunç

Applications and Applied Mathematics: An International Journal (AAM)

This study is concerned with the existence, uniqueness and global exponential stability of weighted pseudo almost periodic solutions of a generalized Nicholson’s blowflies equation with mixed delays. Using some differential inequalities and a fixed point theorem, sufficient conditions were obtained for the existence, uniqueness of at the least a weighted pseudo almost periodic solutions and global exponential stability of this solution. The results of this study are new and complementary to the previous ones can be found in the literature. At the end of the study an example is given to show the accuracy of our results.

A New Method To Solve Fractional Differential Equations: Inverse Fractional Shehu Transform Method, Ali Khalouta, Abdelouahab Kadem

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we propose a new method called the inverse fractional Shehu transform method to solve homogenous and non-homogenous linear fractional differential equations. Fractional derivatives are described in the sense of Riemann-Liouville and Caputo. Illustrative examples are given to demonstrate the validity, efficiency and applicability of the presented method. The solutions obtained by the proposed method are in complete agreement with the solutions available in the literature.

Dynamics In A Respiratory Control Model With Two Delays, Saroj P. Pradhan, Ferenc Hartung, Janos Turi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we study ventilation patterns in a set of parameter dependent nonlinear delay equations with two transport delays modeling the human respiratory control system with peripheral and central control loops. We present a convergent numerical scheme suitable to perform simulations when all disturbances and system parameters are known, then we consider the numerical identifiability of various system parameters based on ventilation data. We are especially interested in the identification of the transport delays in the control loops because these parameters are not measurable directly, but they have a strong influence on system stability/instability.

Boundedness And Square Integrability In Neutral Differential Systems Of Fourth Order, Mebrouk Rahmane, Moussadek Remili, Linda D. Oudjedi

Applications and Applied Mathematics: An International Journal (AAM)

The aim of this paper is to study the asymptotic behavior of solutions to a class of fourth-order neutral differential equations. We discuss the stability, boundedness and square integrability of solutions for the considered system. The technique of proofs involves defining an appropriate Lyapunov functional. Our results obtained in this work improve and extend some existing well-known related results in the relevant literature which were obtained for nonlinear differential equations of fourth order with a constant delay. The obtained results here are new even when our equation is specialized to the forms previously studied and include many recent results in …

Understanding The Fundamental Molecular Mechanism Of Osteogenic Differentiation From Mesenchymal Stem Cells, Imelda Trejo, Hristo V. Kojouharov

Applications and Applied Mathematics: An International Journal (AAM)

A mathematical model is presented to study the regulatory effects of growth factors in osteoblastogenesis. The model incorporates the interactions among mesenchymal stem cells, osteoblasts, and growth factors. The resulting system of nonlinear ordinary differential equations is studied analytically and numerically. Mathematical conditions for successful osteogenic differentiation and optimal osteoblasts population are formulated, which can be used in practice to accelerate bone formation. Numerical simulations are also presented to support the theoretical results and to explore different medical interventions to enhance osteoblastogenesis.

Numerical Solution Of The Lane-Emden Equations With Moving Least Squares Method, Sasan Asadpour, Hassan Hosseinzadeh, Allahbakhsh Yazdani

Applications and Applied Mathematics: An International Journal (AAM)

No abstract provided.

Dynamical Modeling In Cell Biology With Ordinary Differential Equations, Renee Marie Dale

LSU Doctoral Dissertations

Dynamical systems have been of interest to biologists and mathematicians alike. Many processes in biology lend themselves to dynamical study. Movement, change, and response to stimuli are dynamical characteristics that define what is 'alive'. A scientific relationship between these two fields is therefore natural. In this thesis, I describe how my PhD research variously related to biological, mathematical, and computational problems in cell biology. In chapter 1 I introduce some of the current problems in the field. In chapter 2, my mathematical model of firefly luciferase in vivo shows the importance of dynamical models to understand systems. Data originally collected …

The Effects Of Excess Nutrients On Tri-Trophic Food Chains In The Aquatic Ecosystem, Lale Asik, Ming Chen, Angela Peace

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Evaluation Of Age- And Risk-Based Mass Drug Administration Policies To Control Soil-Transmitted Helminths: A Mathematical Modeling Study Of Ghana, Mugdha Thakur

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling And Analysis Of American Chestnut Blight In North America, Robert F. Allen, Anita D. Baines, Hope B. Anderson, John S. Mcalister, Tatum D. Rask, Maia Richards-Dinger

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling Seasonal Dynamics Of Swimmer's Itch And The Efficacy Of Potential Treatment Options, James Peirce

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

The Effect Of External Perturbations On Ecological Oscillators, Eli Goldwyn

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Integrating Mathematics And Biology In The Classroom: A Compendium Of Case Studies And Labs, Becky Sanft, Anne Walter

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.