Ordinary Differential Equations and Applied Dynamics Commons^™

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.

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

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 …

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.

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.

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.

Period Drift In A Neutrally Stable Stochastic Oscillator, Kevin Sanft

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Modeling In Precalculus, Calculus I, And Modeling Courses, Megan Buzby

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Transient Dynamics Of Infection Transmission In An Intensive Care Unit, Christopher Short, Matthew S. Mietchen, Eric T. Lofgren

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Model Of Disease Vector Control With Imperfect Treatment, Bismark Oduro

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Sir Modeling Of American Chestnut Blight, Tatum Rask

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Improving Parasite Transmission Parameters For A Mathematical Model Of Swimmer's Itch Through Both Empirical And Analytical Techniques, Josey Sorenson

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Modeling, Analysis, Simulation Of The Opioid Crisis With Prescription And Social Drug Addiction Models, Kirthi Kumar

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling Collective Migration Of Neural Crest Cells With A Cucker-Smale Velocity Alignment Process, Claire Evensen

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Blood Glucose Regulation: Putting The Pieces Together, Benjamin Zwiener, Margaret Watts

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Cure: A Mathematical Model Of Suicide Risk Among Us Veterans, Anna Singley, Ruth Olson, Sydney Adams, Hannah Callender Highlander

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Multidisciplinary Education And Research In Biomathematics For Solving Global Challenges, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Relaxation And Linear Programs On A Hybrid Control Model, Héctor Jasso-Fuentes, Jose-Luis Menaldi

Mathematics Faculty Research Publications

Some optimality results for hybrid control problems are presented. The hybrid model under study consists of two subdynamics, one of a standard type governed by an ordinary differential equation, and the other of a special type having a discrete evolution. We focus on the case when the interaction between the subdynamics takes place only when the state of the system reaches a given fixed region of the state space. The controller is able to apply two controls, each applied to one of the two subdynamics, whereas the state follows a composite evolution, of continuous type and discrete type. By the …

Remarkable Applications Of Measure Of Non-Compactness For Infinite System Of Differential Equations, Merve İlkhan, Emrah E. Kara

Applications and Applied Mathematics: An International Journal (AAM)

The essential goal of our study is to search for a solution of an infinite system of differential equations in two different Banach spaces under certain assumptions by the aid of measure of noncompactness. Also, we establish some interesting examples related to our results.

Combating Tuberculosis: Using Time-Dependent Sensitivity Analysis To Develop Strategies For Treatment And Prevention, Kendall B. Clark, Mayleen Cortez, Cristian Hernandez, Beth E. Thomas, Allison L. Lewis

Spora: A Journal of Biomathematics

Although many organizations throughout the world have worked tirelessly to control tuberculosis (TB) epidemics, no country has yet been able to eradicate the disease completely. We present two compartmental models representing the spread of a TB epidemic through a population. The first is a general TB model; the second is an adaptation for regions in which HIV is prevalent, accounting for the effects of TB/HIV co-infection. Using active subspaces, we conduct time-dependent sensitivity analysis on both models to explore the significance of certain parameters with respect to the spread of TB. We use the results of this sensitivity analysis to …

Investigation Of Fundamental Principles Of Rigid Body Impact Mechanics, Khalid Alluhydan

Mechanical Engineering Research Theses and Dissertations

In impact mechanics, the collision between two or more bodies is a common, yet a very challenging problem. Producing analytical solutions that can predict the post-collision motion of the colliding bodies require consistent modeling of the dynamics of the colliding bodies. This dissertation presents a new method for solving the two and multibody impact problems that can be used to predict the post-collision motion of the colliding bodies. Also, we solve the rigid body collision problem of planar kinematic chains with multiple contacts with external surfaces.

In the first part of this dissertation, we study planar collisions of Balls and …