Ordinary Differential Equations and Applied Dynamics Commons^™

Mathematical Model Of Competing Nest Founding Strategies By Queen Harvester Ant Pogonomyremex Californicus, Tamantha Pizarro, Yun Kang

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Modeling And Simulation Of Migration Dynamics Of Ukrainian Refugees Due To War In Ukraine 2022-2023, Danielle Sitalo, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling The Communication Dynamics In Human-Autonomy Teams: Insights From Search And Rescue Scenarios, Carlos E. Bustamante Orellana, Lucero Rodriguez Rodriguez, Yun Kang

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Modeling Of The Impact Of Lobbying On Climate Policy, Andrew Jacoby, Claire Hannah, James Hutchinson, Jasmine Narehood, Aditi Ghosh, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Mathematical Model Of Acanthocephalan Parasite Infection In Gull-Billed Terns, Charlotte Moser

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling The Opioid Epidemic: Medicated Versus Non-Medicated Treatment, Gabriel Greenberg, Maniha Akram, Muskan Agarwal

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Effect Of Under-Reporting, Vaccine Efficiency And Social Behavior On Epidemic Progression, Samiran Ghosh

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Fibonacci Differential Equation And Associated Spiral Curves, Mehmet Pakdemirli

CODEE Journal

The Fibonacci differential equation is defined with analogy from the Fibonacci difference equation. The linear second order differential equation is solved for suitable initial conditions. The solutions constitute spirals in the polar coordinates. The properties of the spirals with respect to the Fibonacci numbers and the differences between the new spirals and classical spirals are discussed.

Exploring Parameter Sensitivity Analysis In Mathematical Modeling With Ordinary Differential Equations, Viktoria Savatorova

CODEE Journal

This paper presents an exploration into parameter sensitivity analysis in mathematical modeling using ordinary differential equations (ODEs). Taking the first steps in understanding local sensitivity analysis through the direct differential method and global sensitivity analysis using metrics like Pearson, Spearman, PRCC, and Sobol’, we provide readers with a basic understanding of parameter sensitivity analysis for mathematical modeling using ODEs. As an illustrative application, the system of differential equations modeling population dynamics of several fish species with harvest considerations is utilized. The results of employing local and global sensitivity analysis are compared, shedding light on the strengths and limitations of each …

Rigid Body Constrained Motion Optimization And Control On Lie Groups And Their Tangent Bundles, Brennan S. Mccann

Doctoral Dissertations and Master's Theses

Rigid body motion requires formulations where rotational and translational motion are accounted for appropriately. Two Lie groups, the special orthogonal group SO(3) and the space of quaternions H, are commonly used to represent attitude. When considering rigid body pose, that is spacecraft position and attitude, the special Euclidean group SE(3) and the space of dual quaternions DH are frequently utilized. All these groups are Lie groups and Riemannian manifolds, and these identifications have profound implications for dynamics and controls. The trajectory optimization and optimal control problem on Riemannian manifolds presents significant opportunities for theoretical development. Riemannian optimization is an attractive …

An Implementation Of The Method Of Moments On Chemical Systems With Constant And Time-Dependent Rates, Emmanuel O. Adara, Roger B. Sidje

Northeast Journal of Complex Systems (NEJCS)

Among numerical techniques used to facilitate the analysis of biochemical reactions, we can use the method of moments to directly approximate statistics such as the mean numbers of molecules. The method is computationally viable in time and memory, compared to solving the chemical master equation (CME) which is notoriously expensive. In this study, we apply the method of moments to a chemical system with a constant rate representing a vascular endothelial growth factor (VEGF) model, as well as another system with time-dependent propensities representing the susceptible, infected, and recovered (SIR) model with periodic contact rate. We assess the accuracy of …

Periodic, Nonperiodic, And Chaotic Solutions For A Class Of Difference Equations With Negative Feedback, Benjamin B. Kennedy

Math Faculty Publications

We study the scalar difference equation x(k + 1) = x(k) + (f(x(k - N))) / N,

where f is nonincreasing with negative feedback. This equation is a discretization of the well-studied differential delay equation x'(t) = f(x(t - 1)).

We examine explicit families of such equations for which we can find, for infinitely many values of N and appropriate parameter values, various dynamical behaviors including periodic solutions with large numbers of sign changes per minimal period, solutions that do not converge to periodic solutions, and chaos. We contrast these behaviors with the dynamics of the limiting differential equation. Our …

(R1954) Fractional Order On Modeling The Transmission Of Devastative Covid-19 Infection: Efficacy Of Vaccination, Ashutosh Rajput, Tanvi ., Rajiv Aggarwal, Arpana Sharma, Shiv Kumar Sahdev, Manoj Kumar, Jaimala .

Applications and Applied Mathematics: An International Journal (AAM)

The second wave of COVID-19 is an unprecedented condition in India and began in mid February 2021. Individuals who were already suffering from other comorbidities were found with lung infection, and hence, the number of disease induced deaths were rising faster during the second wave in relation to the first wave. This paper has proposed a mathematical model with fractional order derivatives by correlating the model based number of infectives with the real number of infectives in India. For the system of fractional differential equations, a disease-free state has been computed and proved to be locally asymptotically stable with certain …

(R2033) Resonant Curve Due To Perturbations Of Geo-Synchronous Satellite Including Effect Of Earth’S Equatorial Ellipticity, Sushil Yadav, Mukesh Kumar, Virendra Kumar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we have investigated resonant curve due to frequencies − angular rate of rotation of the Earth and the rate of change of Earth’s equatorial ellipticity parameter. Perturbation equations are used to convert the non-linear equations of motion of geo-synchronous satellite to the linear form. With the help of graphs, we have shown the effect of Earth’s equatorial ellipticity parameter on oscillatory amplitude and variation in orbital radius of satellite. By defining different perturbations, we have also drawn resonant curve due to frequencies steady-state orbital angular rate of satellite and the rate of change of Earth’s equatorial ellipticity …

(R2032) Modeling The Effect Of Sanitation Effort On The Spread Of Carrier-Dependent Infectious Diseases Due To Environmental Degradation, Ram Naresh, Sandhya Rani Verma, J. B. Shukla, Manju Agarwal

Applications and Applied Mathematics: An International Journal (AAM)

In this present study, an SIS model is proposed and analyzed to study the effect of sanitation effort in controlling the spread of carrier-dependent infectious disease in a human habitat due to environmental degradation. The dynamics of the model consist of six dependent variables, the susceptible population density, infective population density, carrier population density, cumulative density of environmental degradation and the density of sanitation effort applied on carrier population and degraded environment. In the modeling process, the carrier population density and sanitation effort are modeled logistically and the degradation of the environment is assumed to be directly proportional to the …

(R2030) Generalized Quasilinearization Method For A Initial Value Problem On Time Scales, Şahap Çetin, Yalçın Yılmaz, Coşkun Yakar

Applications and Applied Mathematics: An International Journal (AAM)

We have investigated that the generalized quasilinearization method under some convenient conditions for nonlinear initial value problem (IVP) of dynamic equation on time scale constructed by monotone sequences of function by using comparison theorem that is the solution of linear IVP of dynamic equation on time scale which converge uniformly and monotonically to the unique solution of the original problem, and the convergence is quadratic.

Deep Hybrid Modeling Of Neuronal Dynamics Using Generative Adversarial Networks, Soheil Saghafi

Dissertations

Mechanistic modeling and machine learning methods are powerful techniques for approximating biological systems and making accurate predictions from data. However, when used in isolation these approaches suffer from distinct shortcomings: model and parameter uncertainty limit mechanistic modeling, whereas machine learning methods disregard the underlying biophysical mechanisms. This dissertation constructs Deep Hybrid Models that address these shortcomings by combining deep learning with mechanistic modeling. In particular, this dissertation uses Generative Adversarial Networks (GANs) to provide an inverse mapping of data to mechanistic models and identifies the distributions of mechanistic model parameters coherent to the data.

Chapter 1 provides background information on …

Modeling The Immune Response To Immunotherapy And Triple Negative Breast Cancer In Mice, Dayton J. Syme, Angelica Davenport, Yun Lu, Anna G. Sorace, Nicholas G. Cogan

Biology and Medicine Through Mathematics Conference

No abstract provided.

Generalized Differential Equation Models For Disease Interventions: A Novel Approach For Predicting Sexually Transmitted Disease Outbreaks, Scott Greenhalgh

Biology and Medicine Through Mathematics Conference

No abstract provided.

Modeling The Dynamics Of Alcohol-Marijuana Co-Abuse In Virginia, Ana L. Vivas-Barber, James Tipton, Sujan Pant, Anne Fernando

Biology and Medicine Through Mathematics Conference

No abstract provided.