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Articles 1 - 19 of 19
Full-Text Articles in Dynamical Systems
Local Lagged Adapted Generalized Method Of Moments Dynamic Process, Gangaram S. Ladde, Olusegun M. Otunuga, Nathan G. Ladde
Local Lagged Adapted Generalized Method Of Moments Dynamic Process, Gangaram S. Ladde, Olusegun M. Otunuga, Nathan G. Ladde
Mathematics Faculty Research
Aspects of a local lagged adapted generalized method of moments (LLGMM) dynamic process are described herein. In one embodiment, the LLGMM process includes obtaining a discrete time data set as past state information of a continuous time dynamic process over a time interval, developing a stochastic model of the continuous time dynamic process, generating a discrete time interconnected dynamic model of local sample mean and variance statistic processes (DTIDMLSMVSP) based on the stochastic model, and calculating a plurality of admissible parameter estimates for the stochastic model using the DTIDMLSMVSP. Further, in some embodiments, the process further includes, for at least …
Quantitative Analysis Of A Stochastic Seitr Epidemic Model With Multiple Stages Of Infection And Treatment, Olusegun M. Otunuga, Mobolaji O. Ogunsolu
Quantitative Analysis Of A Stochastic Seitr Epidemic Model With Multiple Stages Of Infection And Treatment, Olusegun M. Otunuga, Mobolaji O. Ogunsolu
Mathematics Faculty Research
We present a mathematical analysis of the transmission of certain diseases using a stochastic susceptible-exposed-infectious-treated-recovered (SEITR) model with multiple stages of infection and treatment and explore the effects of treatments and external fluctuations in the transmission, treatment and recovery rates. We assume external fluctuations are caused by variability in the number of contacts between infected and susceptible individuals. It is shown that the expected number of secondary infections produced (in the absence of noise) reduces as treatment is introduced into the population. By defining RT,n and ℛT,n as the basic deterministic and stochastic reproduction …
Local Lagged Adapted Generalized Method Of Moments: An Innovative Estimation And Forecasting Approach And Its Applications., Olusegun Michael Otunuga, Gandaram S. Ladde, Nathan G. Ladde
Local Lagged Adapted Generalized Method Of Moments: An Innovative Estimation And Forecasting Approach And Its Applications., Olusegun Michael Otunuga, Gandaram S. Ladde, Nathan G. Ladde
Mathematics Faculty Research
In this work, an attempt is made to apply the Local Lagged Adapted Generalized Method of Moments (LLGMM) to estimate state and parameters in stochastic differential dynamic models. The development of LLGMM is motivated by parameter and state estimation problems in continuous-time nonlinear and non-stationary stochastic dynamic model validation problems in biological, chemical, engineering, energy commodity markets, financial, medical, military, physical sciences and social sciences. The byproducts of this innovative approach (LLGMM) are the balance between model specification and model prescription of continuous-time dynamic process and the development of discrete-time interconnected dynamic model of local sample mean and variance statistic …
Time Varying Parameter Estimation Scheme For A Linear Stochastic Differential Equation, Olusegun Michael Otunuga
Time Varying Parameter Estimation Scheme For A Linear Stochastic Differential Equation, Olusegun Michael Otunuga
Mathematics Faculty Research
In this work, an attempt is made to estimate time varying parameters in a linear stochastic differential equation. By defining mk as the local admissible sample/data observation size at time tk, parameters and state at time tk are estimated using past data on interval [tk−mk+1, tk]. We show that the parameter estimates at each time tk converge in probability to the true value of the parameters being estimated. A numerical simulation is presented by applying the local lagged adapted generalized method of moments (LLGMM) method to the stochastic differential models governing prices of energy …
Controlling Viral Outbreaks: Quantitative Strategies, Anna Mummert, Howard Weiss
Controlling Viral Outbreaks: Quantitative Strategies, Anna Mummert, Howard Weiss
Mathematics Faculty Research
Preparing for and responding to outbreaks of serious livestock infectious diseases are critical measures to safeguard animal health, public health, and food supply. Almost all of the current control strategies are empirical, and mass culling or “stamping out” is frequently the principal strategy for controlling epidemics. However, there are ethical, ecological, and economic reasons to consider less drastic control strategies. Here we use modeling to quantitatively study the efficacy of different control measures for viral outbreaks, where the infectiousness, transmissibility and death rate of animals commonly depends on their viral load. We develop a broad theoretical framework for exploring and …
Global Stability Of Nonlinear Stochastic Sei Epidemic Model With Fluctuations In Transmission Rate Of Disease, Olusegun Michael Otunuga
Global Stability Of Nonlinear Stochastic Sei Epidemic Model With Fluctuations In Transmission Rate Of Disease, Olusegun Michael Otunuga
Mathematics Faculty Research
We derive and analyze the dynamic of a stochastic SEI epidemic model for disease spread. Fluctuations in the transmission rate of the disease bring about stochasticity in model. We discuss the asymptotic stability of the infection-free equilibrium by first deriving the closed form deterministic (R0) and stochastic (R0) basic reproductive number. Contrary to some author’s remark that different diffusion rates have no effect on the stability of the disease-free equilibrium, we showed that even if no epidemic invasion occurs with respect to the deterministic version of the SEI model (i.e., R0 < 1), epidemic can still grow initially (if R0 > 1) …
Local Sensitivity Analysis Of Acute Inflammation, James Martin
Local Sensitivity Analysis Of Acute Inflammation, James Martin
Theses, Dissertations and Capstones
The inflammatory response is the body's response to some pathogen or foreign invader. When infected by a pathogen, a healthy individual will mount a response with immunological factors to eliminate it. An inflammatory response that is either too strong or too weak can be detrimental to the individual's health. We will look at a qualitative mathematical model of the inflammatory response, in scenarios that represent varying disorders of the immune system. Using sensitivity analysis we determine which parameters of this model are most influential in the different scenarios. By determining which parameters are most influential we can suggest possible targets …
Local Lagged Adapted Generalized Method Of Moments And Applications, Olusegun Michael Otunuga, Gangaram S. Ladde, Nathan G. Ladde
Local Lagged Adapted Generalized Method Of Moments And Applications, Olusegun Michael Otunuga, Gangaram S. Ladde, Nathan G. Ladde
Mathematics Faculty Research
In this work, an attempt is made for developing the local lagged adapted generalized method of moments (LLGMM). This proposed method is composed of: (1) development of the stochastic model for continuous-time dynamic process, (2) development of the discrete-time interconnected dynamic model for statistic process, (3) utilization of Euler-type discretized scheme for nonlinear and non-stationary system of stochastic differential equations, (4) development of generalized method of moment/observation equations by employing lagged adaptive expectation process, (5) introduction of the conceptual and computational parameter estimation problem, (6) formulation of the conceptual and computational state estimation scheme and (7) definition of the conditional …
A Mechanical Investigation Of Second Order Homogeneous Dynamic Equations On A Time Scale, Jacob E. Fischer
A Mechanical Investigation Of Second Order Homogeneous Dynamic Equations On A Time Scale, Jacob E. Fischer
Theses, Dissertations and Capstones
This thesis covers the basic aspects of time scale calculus, a branch of mathematics combining the theories of differential equations and difference equations. Using the properties of time scale calculus we analyze a second order homogeneous dynamic equation with constant coefficients, in particular, y ∆∆ − 1 6 y ∆ + 1 8 y = 0. Following the analysis, this problem will be graphically evaluated using Marshall University’s Differential Analyzer, affectionately named Art. A differential analyzer is a machine that mechanically integrates by way of related rates of rotating rods. The process for making the jump between intervals on a …
Stochastic Modeling Of Energy Commodity Spot Price Processes With Delay In Volatility, Olusegun Michael Otunuga, Gangaram S. Ladde
Stochastic Modeling Of Energy Commodity Spot Price Processes With Delay In Volatility, Olusegun Michael Otunuga, Gangaram S. Ladde
Mathematics Faculty Research
Employing basic economic principles, we systematically develop both deterministic and stochastic dynamic models for the log-spot price process of energy commodity. Furthermore, treating a diffusion coefficient parameter in the non-seasonal log-spot price dynamic system as a stochastic volatility functional of log-spot price, an interconnected system of stochastic model for log-spot price, expected log-spot price and hereditary volatility process is developed. By outlining the risk-neutral dynamics and pricing, sufficient conditions are given to guarantee that the risk-neutral dynamic model is equivalent to the developed model. Furthermore, it is shown that the expectation of the square of volatility under the risk-neutral measure …
Mechanical Visualization Of A Second Order Dynamic Equation On Varying Time Scales, Molly Kathryn Peterson
Mechanical Visualization Of A Second Order Dynamic Equation On Varying Time Scales, Molly Kathryn Peterson
Theses, Dissertations and Capstones
In this work, we give an introduction to Time Scales Calculus, the properties of the exponential function on an arbitrary time scale, and use it to solve linear dynamic equation of second order. Time Scales Calculus was introduced by Stefan Hilger in 1988. It brings together the theories of difference and differential equations into one unified theory. By using the properties of the delta derivative and the delta anti-derivative, we analyze the behavior of a second order linear homogeneous dynamic equation on various time scales. After the analytical discussion, we will graphically evaluate the second order dynamic equation in Marshall’s …
Solutions Of Dynamic Equations On Time Scales With Jumps, Kayode Daniel Olumoyin
Solutions Of Dynamic Equations On Time Scales With Jumps, Kayode Daniel Olumoyin
Theses, Dissertations and Capstones
To obtain the solution of first order dynamic equations on time scales with jumps, a good question to ask is, how many initial conditions will be needed? We shall show that you only need the initial condition that gives you either the initial position or the initial velocity. The solution at each left scattered point in the time scale can be obtained analytically. With this approach we shall write the general form of the solution of a first order dynamic equations on time scales with jumps. To do this we shall use the Hilger derivative, anti-derivatives, the Hilger Complex plane, …
Finding Positive Solutions Of Boundary Value Dynamic Equations On Time Scale, Olusegun Michael Otunuga
Finding Positive Solutions Of Boundary Value Dynamic Equations On Time Scale, Olusegun Michael Otunuga
Theses, Dissertations and Capstones
This thesis is on the study of dynamic equations on time scale. Most often, the derivatives and anti-derivatives of functions are taken on the domain of real numbers, which cannot be used to solve some models like insect populations that are continuous while in season and then follow a difference scheme with variable step-size. They die out in winter, while the eggs are incubating or dormant; and then they hatch in a new season, giving rise to a non overlapping population. The general idea of my thesis is to find the conditions for having a positive solution of any boundary …
Variable Shape Parameter Strategies In Radial Basis Function Methods, Derek Sturgill
Variable Shape Parameter Strategies In Radial Basis Function Methods, Derek Sturgill
Theses, Dissertations and Capstones
The Radial Basis Function (RBF) method is an important tool in the interpolation of multidimensional scattered data. The method has several important properties. One is the ability to handle sparse and scattered data points. Another property is its ability to interpolate in more than one dimension. Furthermore, the Radial Basis Function method provides phenomenal accuracy which has made it very popular in many fields. Some examples of applications using the RBF method are numerical solutions to partial differential equations, image processing, and cartography. This thesis involves researching Radial Basis Functions using different shape parameter strategies. First, we introduce the Radial …
Non-Preemptive Shunting In M/M/1 And Dynamic Service Queueing Systems, Steven Lacek
Non-Preemptive Shunting In M/M/1 And Dynamic Service Queueing Systems, Steven Lacek
Theses, Dissertations and Capstones
We provide a study of two queueing systems, namely, an M/M/1 queueing system in which an incoming customer shunts, or skips line, and a dynamic server in an infinite capacity system moving among service nodes. In the former, we explore various aspects of the system, including waiting time, and the relationships between shunting and position in queue and rate of service. Through use of global balance equations, we find the probability that an arriving non-priority customer, finding customers waiting in the system, will shunt to a position other than behind the queue. In the latter, we explore a system in …
Geometric Field Stability And Normal Field Curvature Of Solution Sets Of Ordinary Differential Equations In Two Variables, Leslie L. Kerns
Geometric Field Stability And Normal Field Curvature Of Solution Sets Of Ordinary Differential Equations In Two Variables, Leslie L. Kerns
Theses, Dissertations and Capstones
The classical linearization approach to stability theory determines whether or not a system is stable in the vicinity of its equilibrium points. This classical approach partly depends on the validity of the linear approximation. The definition of stability developed in this article takes a different approach and uses a curvature function to assess the relative locations of solutions within a field of solutions (the underlying solution set of the ODE). The present approach involves calculations that directly yield stability information, without having to enter into the often lengthy eigenvalue-eigenvector method. The present results both complement and are compatible with the …
The Dynamics Of Newton's Method On Cubic Polynomials, Shannon N. Miller
The Dynamics Of Newton's Method On Cubic Polynomials, Shannon N. Miller
Theses, Dissertations and Capstones
The field of dynamics is itself a huge part of many branches of science, including the motion of the planets and galaxies, changing weather patterns, and the growth and decline of populations. Consider a function f and pick x0 in the domain of f . If we iterate this function around the point x0, then we will have the sequence x0, f (x0), f (f (x0)), f (f (f (x0))), ..., which becomes our dynamical system. We are essentially interested in the end behavior of this system. Do …
Solving Higher Order Dynamic Equations On Time Scales As First Order Systems, Elizabeth R. Duke
Solving Higher Order Dynamic Equations On Time Scales As First Order Systems, Elizabeth R. Duke
Theses, Dissertations and Capstones
Time scales calculus seeks to unite two disparate worlds: that of differential, Newtonian calculus and the difference calculus. As such, in place of differential and difference equations, time scales calculus uses dynamic equations. Many theoretical results have been developed concerning solutions of dynamic equations. However, little work has been done in the arena of developing numerical methods for approximating these solutions. This thesis work takes a first step in obtaining numerical solutions of dynamic equations|a protocol for writing higher-order dynamic equations as systems of first-order equations. This process proves necessary in obtaining numerical solutions of differential equations since the Runge-Kutta …
Dynamic Equations On Changing Time Scales: Dynamics Of Given Logistic Problems, Parameterization, And Convergence Of Solutions, Kelli J. Hall
Dynamic Equations On Changing Time Scales: Dynamics Of Given Logistic Problems, Parameterization, And Convergence Of Solutions, Kelli J. Hall
Theses, Dissertations and Capstones
In this thesis we use the theory of dynamic equations on time scales to understand the changes in dynamics between difference and differen- tial equations by parameterizing the underlying domains. To illustrate where and how these changes occur, we then construct a bifurcation diagram for a simple family of dynamic equations. However, these results are only true if we can move continuously through our domains, i.e, the time scales. In the last part of this thesis, we define what it means to have a convergent sequence of time scales. Then we use this definition to prove that the limit …