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 Title
 ANALYTICAL AND NUMERICAL SOLUTIONS OF DIFFERENTIALEQUATIONS ARISING IN FLUID FLOW AND HEAT TRANSFER PROBLEMS.
 Creator

Sweet, Erik, Vajravelu, Kuppalapalle, University of Central Florida
 Abstract / Description

The solutions of nonlinear ordinary or partial differential equations are important in the study of fluid flow and heat transfer. In this thesis we apply the Homotopy Analysis Method (HAM) and obtain solutions for several fluid flow and heat transfer problems. In chapter 1, a brief introduction to the history of homotopies and embeddings, along with some examples, are given. The application of homotopies and an introduction to the solutions procedure of differential equations (used in the...
Show moreThe solutions of nonlinear ordinary or partial differential equations are important in the study of fluid flow and heat transfer. In this thesis we apply the Homotopy Analysis Method (HAM) and obtain solutions for several fluid flow and heat transfer problems. In chapter 1, a brief introduction to the history of homotopies and embeddings, along with some examples, are given. The application of homotopies and an introduction to the solutions procedure of differential equations (used in the thesis) are provided. In the chapters that follow, we apply HAM to a variety of problems to highlight its use and versatility in solving a range of nonlinear problems arising in fluid flow. In chapter 2, a viscous fluid flow problem is considered to illustrate the application of HAM. In chapter 3, we explore the solution of a nonNewtonian fluid flow and provide a proof for the existence of solutions. In addition, chapter 3 sheds light on the versatility and the ease of the application of the Homotopy Analysis Method, and its capability in handling nonlinearity (of rational powers). In chapter 4, we apply HAM to the case in which the fluid is flowing along stretching surfaces by taking into the effects of "slip" and suction or injection at the surface. In chapter 5 we apply HAM to a Magnetohydrodynamic fluid (MHD) flow in two dimensions. Here we allow for the fluid to flow between two plates which are allowed to move together or apart. Also, by considering the effects of suction or injection at the surface, we investigate the effects of changes in the fluid density on the velocity field. Furthermore, the effect of the magnetic field is considered. Chapter 6 deals with MHD fluid flow over a sphere. This problem gave us the first opportunity to apply HAM to a coupled system of nonlinear differential equations. In chapter 7, we study the fluid flow between two infinite stretching disks. Here we solve a fourth order nonlinear ordinary differential equation. In chapter 8, we apply HAM to a nonlinear system of coupled partial differential equations known as the Drinfeld Sokolov equations and bring out the effects of the physical parameters on the traveling wave solutions. Finally, in chapter 9, we present prospects for future work.
Show less  Date Issued
 2009
 Identifier
 CFE0002889, ucf:48017
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0002889
 Title
 Analytical solutions to nonlinear differential equations arising in physical problems.
 Creator

Baxter, Mathew, Vajravelu, Kuppalapalle, Li, Xin, Mohapatra, Ram, Shuai, Zhisheng, Kassab, Alain, University of Central Florida
 Abstract / Description

Nonlinear partial differential equations are difficult to solve, with many of the approximate solutions in the literature being numerical in nature. In this work, we apply the Homotopy Analysis Method to give approximate analytical solutions to nonlinear ordinary and partial differential equations. The main goal is to apply different linear operators, which can be chosen, to solve nonlinear problems. In the first three chapters, we study ordinary differential equations (ODEs) with one or two...
Show moreNonlinear partial differential equations are difficult to solve, with many of the approximate solutions in the literature being numerical in nature. In this work, we apply the Homotopy Analysis Method to give approximate analytical solutions to nonlinear ordinary and partial differential equations. The main goal is to apply different linear operators, which can be chosen, to solve nonlinear problems. In the first three chapters, we study ordinary differential equations (ODEs) with one or two linear operators. As we progress, we apply the method to partial differential equations (PDEs) and use several linear operators. The results are all purely analytical, meaning these are approximate solutions that we can evaluate at points and take their derivatives.Another main focus is error analysis, where we test how good our approximations are. The method will always produce approximations, but we use residual errors on the domain of the problem to find a measure of error.In the last two chapters, we apply similarity transforms to PDEs to transform them into ODEs. We then use the Homotopy Analysis Method on one, but are able to find exact solutions to both equations.
Show less  Date Issued
 2014
 Identifier
 CFE0005303, ucf:50527
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0005303
 Title
 Modeling Network Worm Outbreaks.
 Creator

Foley, Evan, Shuai, Zhisheng, Kaup, David, Nevai, A, University of Central Florida
 Abstract / Description

Due to their convenience, computers have become a standard in society and therefore, need the utmost care. It is convenient and useful to model the behavior of digital virus outbreaks that occur, globally or locally. Compartmental models will be used to analyze the mannerisms and behaviors of computer malware. This paper will focus on a computer worm, a type of malware, spread within a business network. A mathematical model is proposed consisting of four compartments labeled as Susceptible,...
Show moreDue to their convenience, computers have become a standard in society and therefore, need the utmost care. It is convenient and useful to model the behavior of digital virus outbreaks that occur, globally or locally. Compartmental models will be used to analyze the mannerisms and behaviors of computer malware. This paper will focus on a computer worm, a type of malware, spread within a business network. A mathematical model is proposed consisting of four compartments labeled as Susceptible, Infectious, Treatment, and Antidotal. We shall show that allocating resources into treating infectious computers leads to a reduced peak of infections across the infection period, while pouring resources into treating susceptible computers decreases the total amount of infections throughout the infection period. This is assuming both methods are receiving resources without loss. This result reveals an interesting notion of balance between protecting computers and removing computers from infections, ultimately depending on the business executives' goals and/or preferences.
Show less  Date Issued
 2015
 Identifier
 CFE0005948, ucf:50816
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0005948
 Title
 A NUMERICAL ANALYSIS APPROACH FOR ESTIMATING THE MINIMUM TRAVELING WAVE SPEED FOR AN AUTOCATALYTIC REACTION.
 Creator

Blanken, Erika, Qi, Yuanwei, University of Central Florida
 Abstract / Description

This thesis studies the traveling wavefront created by the autocatalytic cubic chemical reaction A + 2B → 3B involving two chemical species A and B, where A is the reactant and B is the autocatalyst. The diffusion coefficients for A and B are given by and . These coefficients differ as a result of the chemical species having different size and/or weight. Theoretical results show there exist bounds, and , depending on , where for speeds , a traveling wave solution exists, while for speeds , a...
Show moreThis thesis studies the traveling wavefront created by the autocatalytic cubic chemical reaction A + 2B → 3B involving two chemical species A and B, where A is the reactant and B is the autocatalyst. The diffusion coefficients for A and B are given by and . These coefficients differ as a result of the chemical species having different size and/or weight. Theoretical results show there exist bounds, and , depending on , where for speeds , a traveling wave solution exists, while for speeds , a solution does not exist. Moreover, if , and are similar to one another and in the order of when it is small. On the other hand, when there exists a minimum speed vmin, such that there is a traveling wave solution if the speed v > vmin. The determination of vmin is very important in determining the dynamics of general solutions. To fill in the gap of the theoretical study, we use numerical methods to determine vmin for various cases. The numerical algorithm used is the fourthorder RungeKutta method (RK4).
Show less  Date Issued
 2008
 Identifier
 CFE0002061, ucf:47571
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0002061
 Title
 AN EXAMINATION OF THE EFFECTIVENESS OF THE ADOMIAN DECOMPOSITION METHOD IN FLUID DYNAMIC APPLICATIONS.
 Creator

Holmquist, Sonia, Mohapatra, Ram, University of Central Florida
 Abstract / Description

Since its introduction in the 1980's, the Adomian Decomposition Method (ADM) has proven to be an efficient and reliable method for solving many types of problems. Originally developed to solve nonlinear functional equations, the ADM has since been used for a wide range of equation types (like boundary value problems, integral equations, equations arising in flow of incompressible and compressible fluids etc...). This work is devoted to an evaluation of the effectiveness of this method...
Show moreSince its introduction in the 1980's, the Adomian Decomposition Method (ADM) has proven to be an efficient and reliable method for solving many types of problems. Originally developed to solve nonlinear functional equations, the ADM has since been used for a wide range of equation types (like boundary value problems, integral equations, equations arising in flow of incompressible and compressible fluids etc...). This work is devoted to an evaluation of the effectiveness of this method when used for fluid dynamic applications. In particular, the ADM has been applied to the Blasius equation, the FalknerSkan equation, and the OrrSommerfeld equation. This study is divided into five Chapters and an Appendix. The first chapter is devoted to an introduction of the Adomian Decomposition method (ADM) with simple illustrations. The Second Chapter is devoted to the application of the ADM to generalized Blasius Equation and our result is compared to other published results when the parameter values are appropriately set. Chapter 3 presents the solution generated for the FalknerSkan equation. Finally, the OrrSommerfeld equation is dealt with in the fourth Chapter. Chapter 5 is devoted to the findings and recommendations based on this study. The Appendix contains details of the solutions considered as well as an alternate solution for the generalized Blasius Equation using Bender's deltaperturbation method.
Show less  Date Issued
 2007
 Identifier
 CFE0001735, ucf:47318
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0001735
 Title
 SOLITARY WAVE FAMILIES IN TWO NONINTEGRABLE MODELS USING REVERSIBLE SYSTEMS THEORY.
 Creator

Leto, Jonathan, Choudhury, S. Roy, University of Central Florida
 Abstract / Description

In this thesis, we apply a recently developed technique to comprehensively categorize all possible families of solitary wave solutions in two models of topical interest. The models considered are: a) the Generalized PochhammerChree Equations, which govern the propagation of longitudinal waves in elastic rods, and b) a generalized microstructure PDE. Limited analytic results exist for the occurrence of one family of solitary wave solutions for each of these equations. Since, as mentioned...
Show moreIn this thesis, we apply a recently developed technique to comprehensively categorize all possible families of solitary wave solutions in two models of topical interest. The models considered are: a) the Generalized PochhammerChree Equations, which govern the propagation of longitudinal waves in elastic rods, and b) a generalized microstructure PDE. Limited analytic results exist for the occurrence of one family of solitary wave solutions for each of these equations. Since, as mentioned above, solitary wave solutions often play a central role in the longtime evolution of an initial disturbance, we consider such solutions of both models here (via the normal form approach) within the framework of reversible systems theory. Besides confirming the existence of the known family of solitary waves for each model, we find a continuum of delocalized solitary waves (or homoclinics to smallamplitude periodic orbits). On isolated curves in the relevant parameter region, the delocalized waves reduce to genuine embedded solitons. For the microstructure equation, the new family of solutions occur in regions of parameter space distinct from the known solitary wave solutions and are thus entirely new. Directions for future work, including the dynamics of each family of solitary waves using exponential asymptotics techniques, are also mentioned.
Show less  Date Issued
 2008
 Identifier
 CFE0002151, ucf:47930
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0002151
 Title
 Nonlinear dispersive partial differential equations of physical relevance with applications to vortex dynamics.
 Creator

VanGorder, Robert, Kaup, David, Vajravelu, Kuppalapalle, Nevai, Andrew, Mohapatra, Ram, Kassab, Alain, University of Central Florida
 Abstract / Description

Nonlinear dispersive partial differential equations occur in a variety of areas within mathematical physics and engineering. We study several classes of such equations, including scalar complex partial differential equations, vector partial differential equations, and finally nonlocal integrodifferential equations. For physically interesting families of these equations, we demonstrate the existence (and, when possible, stability) of specific solutions which are relevant for applications....
Show moreNonlinear dispersive partial differential equations occur in a variety of areas within mathematical physics and engineering. We study several classes of such equations, including scalar complex partial differential equations, vector partial differential equations, and finally nonlocal integrodifferential equations. For physically interesting families of these equations, we demonstrate the existence (and, when possible, stability) of specific solutions which are relevant for applications. While multiple application areas are considered, the primary application that runs through the work would be the nonlinear dynamics of vortex filaments under a variety of physical models. For instance, we are able to determine the structure and time evolution of several physical solutions, including the planar, helical, selfsimilar and soliton vortex filament solutions in a quantum fluid. Properties of such solutions are determined analytically and numerically through a variety of approaches. Starting with complex scalar equations (often useful for studying twodimensional motion), we progress through more complicated models involving vector partial differential equations and nonlocal equations (which permit motion in three dimensions). In many of the examples considered, the qualitative analytical results are used to verify behaviors previously observed only numerically or experimentally.
Show less  Date Issued
 2014
 Identifier
 CFE0005272, ucf:50545
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0005272
 Title
 MATHEMATICAL MODELS OF MOSQUITO POPULATIONS.
 Creator

Reed, Hanna, Shuai, Zhisheng, University of Central Florida
 Abstract / Description

The intent of this thesis is to develop ordinary differential equation models to better understand the mosquito population. We first develop a framework model, where we determine the condition under which a natural mosquito population can persist in the environment. Wolbachia is a bacterium which limits the replication of viruses inside the mosquito which it infects. As a result, infecting a mosquito population with Wolbachia can decrease the transmission of viral mosquitoborne diseases,...
Show moreThe intent of this thesis is to develop ordinary differential equation models to better understand the mosquito population. We first develop a framework model, where we determine the condition under which a natural mosquito population can persist in the environment. Wolbachia is a bacterium which limits the replication of viruses inside the mosquito which it infects. As a result, infecting a mosquito population with Wolbachia can decrease the transmission of viral mosquitoborne diseases, such as dengue. We develop another ODE model to investigate the invasion of Wolbachia in a mosquito population. In a biologically feasible situation, we determine three coexisting equilibria: a stable Wolbachiafree equilibrium, an unstable coexistence equilibrium, and a complete invasion equilibrium. We establish the conditions under which a population of Wolbachia infected mosquitoes may persist in the environment via the next generation number and determine when a natural mosquito population may experience a complete invasion of Wolbachia.
Show less  Date Issued
 2018
 Identifier
 CFH2000299, ucf:45845
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFH2000299
 Title
 Analytical and Numerical Investigations of the Kudryashov Generalized KdV Equation.
 Creator

Hilton, William, Schober, Constance, Moore, Brian, Choudhury, Sudipto, University of Central Florida
 Abstract / Description

This thesis concerns an analytical and numerical study of the Kudryashov Generalized Kortewegde Vries (KG KdV) equation. Using a refined perturbation expansion of the FermiPastaUlam (FPU) equations of motion, the KG KdV equation, which arises at sixth order, and general higher order KdV equations are derived. Special solutions of the KG KdV equation are derived using the tanh method. A pseudospectral integrator, which can handle stiff equations, is developed for the higher order KdV...
Show moreThis thesis concerns an analytical and numerical study of the Kudryashov Generalized Kortewegde Vries (KG KdV) equation. Using a refined perturbation expansion of the FermiPastaUlam (FPU) equations of motion, the KG KdV equation, which arises at sixth order, and general higher order KdV equations are derived. Special solutions of the KG KdV equation are derived using the tanh method. A pseudospectral integrator, which can handle stiff equations, is developed for the higher order KdV equations. The numerical experiments indicate that although the higher order equations exhibit complex dynamics, they fail to reach energy equipartition on the time scale considered.
Show less  Date Issued
 2018
 Identifier
 CFE0007754, ucf:52395
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0007754
 Title
 Structurepreserving finite difference methods for linearly damped differential equations.
 Creator

Bhatt, Ashish, Moore, Brian, Choudhury, Sudipto, Gurel, Basak, Kauffman, Jeffrey L., University of Central Florida
 Abstract / Description

Differential equations (DEs) model a variety of physical phenomena in science and engineering. Many physical phenomena involve conservative or dissipative forces, which manifest themselves as qualitative properties of DEs that govern these phenomena. Since only a few and simplistic models are known to have exact solutions, approximate solution techniques, such as numerical integration, are used to reveal important insights about solution behavior and properties of these models. Numerical...
Show moreDifferential equations (DEs) model a variety of physical phenomena in science and engineering. Many physical phenomena involve conservative or dissipative forces, which manifest themselves as qualitative properties of DEs that govern these phenomena. Since only a few and simplistic models are known to have exact solutions, approximate solution techniques, such as numerical integration, are used to reveal important insights about solution behavior and properties of these models. Numerical integrators generally result in undesirable quantitative and qualitative errors . Standard numerical integrators aim to reduce quantitative errors, whereas geometric (numerical) integrators aim to reduce or eliminate qualitative errors, as well, in order to improve the accuracy of numerical solutions. It is now widely recognized that geometric (or structurepreserving) integrators are advantageous compared to nongeometric integrators for DEs, especially for long time integration.Geometric integrators for conservative DEs have been proposed, analyzed, and investigated extensively in the literature. The motif of this thesis is to extend the idea of structure preservation to linearly damped DEs. More specifically, we develop, analyze, and implement geometric integrators for linearly damped ordinary and partial differential equations (ODEs and PDEs) that possess conformal invariants, which are qualitative properties that decay exponentially along any solution of the DE as the system evolves over time. In particular, we derive restrictions on the coefficient functions of exponential RungeKutta (ERK) numerical methods for preservation of certain conformal invariants of linearly damped ODEs. An important class of these methods is shown to preserve the damping rate of solutions of damped linear ODEs. Linearly stability and order of accuracy for some specific cases of ERK methods are investigated. Geometric integrators for PDEs are designed using structurepreserving ERK methods in space, time, or both. These integrators for PDEs are also shown to preserve additional structure in certain special cases. Numerical experiments illustrate higher order accuracy and structure preservation properties of various ERK based methods, demonstrating clear advantages over nonstructurepreserving methods, as well as usefulness for solving a wide range of DEs.
Show less  Date Issued
 2016
 Identifier
 CFE0006832, ucf:51763
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0006832
 Title
 STANDING WAVES OF SPATIALLY DISCRETE FITZHUGHNAGUMO EQUATIONS.
 Creator

Segal, Joseph, Moore, Brian, University of Central Florida
 Abstract / Description

We study a system of spatially discrete FitzHughNagumo equations, which are nonlinear differentialdifference equations on an infinite onedimensional lattice. These equations are used as a model of impulse propagation in nerve cells. We employ McKean's caricature of the cubic as our nonlinearity, which allows us to reduce the nonlinear problem into a linear inhomogeneous problem. We find exact solutions for standing waves, which are steady states of the system. We derive formulas for...
Show moreWe study a system of spatially discrete FitzHughNagumo equations, which are nonlinear differentialdifference equations on an infinite onedimensional lattice. These equations are used as a model of impulse propagation in nerve cells. We employ McKean's caricature of the cubic as our nonlinearity, which allows us to reduce the nonlinear problem into a linear inhomogeneous problem. We find exact solutions for standing waves, which are steady states of the system. We derive formulas for all 1pulse solutions. We determine the range of parameter values that allow for the existence of standing waves. We use numerical methods to demonstrate the stability of our solutions and to investigate the relationship between the existence of standing waves and propagation failure of traveling waves.
Show less  Date Issued
 2009
 Identifier
 CFE0002892, ucf:48021
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0002892
 Title
 The Response of American Police Agencies to Digital Evidence.
 Creator

Yesilyurt, Hamdi, Wan, Thomas, Potter, Roberto, Applegate, Brandon, Lang, SheauDong, University of Central Florida
 Abstract / Description

Little is known about the variation in digital forensics practice in the United States as adopted by large local police agencies. This study investigated how environmental constraints, contextual factors, organizational complexity, and organizational control relate to the adoption of digital forensics practice. This study integrated 3 theoretical perspectives in organizational studies to guide the analysis of the relations: institutional theory, contingency theory, and adoptionofinnovation...
Show moreLittle is known about the variation in digital forensics practice in the United States as adopted by large local police agencies. This study investigated how environmental constraints, contextual factors, organizational complexity, and organizational control relate to the adoption of digital forensics practice. This study integrated 3 theoretical perspectives in organizational studies to guide the analysis of the relations: institutional theory, contingency theory, and adoptionofinnovation theory. Institutional theory was used to analyze the impact of environmental constraints on the adoption of innovation, and contingency theory was used to examine the impacts of organizational control on the adoption of innovation. Adoption of innovation theory was employed to describe the degree to which digital forensics practice has been adopted by large municipal police agencies having 100 or more sworn police officers.The data set was assembled primarily by using Law Enforcement Management and Administrative Statistics (LEMAS) 2003 and 1999. Dr. Edward Maguire`s survey was used to obtain 1 variable. The joining up of the data set to construct the sample resulted in 345 large local police agencies. The descriptive results on the degree of adoption of digital forensics practice indicate that 37.7% of large local police agencies have dedicated personnel to address digital evidence, 32.8% of police agencies address digital evidence but do not have dedicated personnel, and only 24.3% of police agencies have a specialized unit with fulltime personnel to address digital evidence. About 5% of local police agencies do nothing to address digital evidence in any circumstance. These descriptive statistics indicate that digital evidence is a matter of concern for most large local police agencies and that they respond to varying degrees to digital evidence at the organizational level. Agencies that have not adopted digital forensics practice are in the minority. The structural equation model was used to test the hypothesized relations, easing the rigorous analysis of relations between latent constructs and several indicator variables. Environmental constraints have the largest impact on the adoption of innovation, exerting a positive influence. No statistically significant relation was found between organizational control and adoption of digital forensic practice. Contextual factors (task scope and personnel size) positively influence the adoption of digital forensics. Structural control factors, including administrative weight and formalization, have no significant influence on the adoption of innovation. The conclusions of the study are as follows. Police agencies adopt digital forensics practice primarily by relying on environmental constraints. Police agencies exposed to higher environmental constraints are more frequently expected to adopt digital forensics practice. Because organizational control of police agencies is not significantly related to digital forensics practice adoption, police agencies do not take their organizational control extensively into consideration when they consider adopting digital forensics practice. The positive influence of task scope and size on digital forensics practice adoption was expected. The extent of task scope and the number of personnel indicate a higher capacity for police agencies to adopt digital forensics practice. Administrative weight and formalization do not influence the adoption of digital forensics practice. Therefore, structural control and coordination are not important for large local police agencies to adopt digital forensics practice.The results of the study indicate that the adoption of digital forensics practice is based primarily on environmental constraints. Therefore, more drastic impacts on digital forensics practice should be expected from local police agencies' environments than from internal organizational factors. Researchers investigating the influence of various factors on the adoption of digital forensics practice should further examine environmental variables. The unexpected results concerning the impact of administrative weight and formalization should be researched with broader considerations.
Show less  Date Issued
 2011
 Identifier
 CFE0004181, ucf:49081
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004181
 Title
 A mathematical model for feral cat ecology with application to disease.
 Creator

Sharpe, Jeff, Nevai, A, Shuai, Zhisheng, Qi, Yuanwei, QuintanaAscencio, Pedro, University of Central Florida
 Abstract / Description

We formulate and analyze a mathematical model for feral cats living in an isolated colony. The model contains compartments for kittens, adult females and adult males. Kittens are born at a rate proportional to the population of adult females and mature at equal rates into adult females and adult males. Adults compete with each other in a manner analogous to LotkaVolterra competition. This competition comes in four forms, classified by gender. Native house cats, and their effects are also...
Show moreWe formulate and analyze a mathematical model for feral cats living in an isolated colony. The model contains compartments for kittens, adult females and adult males. Kittens are born at a rate proportional to the population of adult females and mature at equal rates into adult females and adult males. Adults compete with each other in a manner analogous to LotkaVolterra competition. This competition comes in four forms, classified by gender. Native house cats, and their effects are also considered, including additional competition and abandonment into the feral population. Control measures are also modeled in the form of percapita removal rates. We compute the net reproduction number (R_0) for the colony and consider its influence. In the absence of abandonment, if R_0(>)1, the population always persists at a positive equilibrium and if R_0 (<)= 1, the population always tends toward local extinction. This work will be referred to as the core model.The model is then expanded to include a set of colonies (patches) such as those in the core model (this time neglecting the effect of abandonment). Adult females and kittens remain in their native patch while adult males spend a fixed proportion of their time in each patch. Adult females experience competition from both the adult females living in the same patch as well as the visiting adult males. The proportion of adult males in patch j suffer competition from both adult females resident to that patch as well the proportion of adult males also in the patch. We formulate a net reproduction number for each patch (a patch reproduction number) R_j. If R_j(>)1 for at least one patch, then the collective population always persists at some nontrivial (but possibly semitrivial) steady state. We consider the number of possible steady states and their properties. This work will be referred to as the patch model.Finally, the core model is expanded to include the introduction of the feline leukemia virus. Since this disease has many modes of transmission, each of which depends on the host's gender and lifestage, we regard this as a model disease. A basic reproduction number R_0 for the disease is defined and analyzed. Vaccination terms are included and their role in disease propagation is analyzed. Necessary and sufficient conditions are given under which the diseasefree equilibrium is stable.
Show less  Date Issued
 2016
 Identifier
 CFE0006502, ucf:51389
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0006502
 Title
 AN ALLAGAINSTONE GAME APPROACH FOR THE MULTIPLAYER PURSUITEVASION PROBLEM.
 Creator

Talebi, Shahriar, Simaan, Marwan, Qu, Zhihua, Vosoughi, Azadeh, University of Central Florida
 Abstract / Description

The traditional pursuitevasion game considers a situation where one pursuer tries to capture an evader, while the evader is trying to escape. A more general formulation of this problem is to consider multiple pursuers trying to capture one evader. This general multipursuer oneevader problem can also be used to model a system of systems in which one of the subsystems decides to dissent (evade) from the others while the others (the pursuer subsystems) try to pursue a strategy to prevent it...
Show moreThe traditional pursuitevasion game considers a situation where one pursuer tries to capture an evader, while the evader is trying to escape. A more general formulation of this problem is to consider multiple pursuers trying to capture one evader. This general multipursuer oneevader problem can also be used to model a system of systems in which one of the subsystems decides to dissent (evade) from the others while the others (the pursuer subsystems) try to pursue a strategy to prevent it from doing so. An important challenge in analyzing these types of problems is to develop strategies for the pursuers along with the advantages and disadvantages of each. In this thesis, we investigate three possible and conceptually different strategies for pursuers: (1) act noncooperatively as independent pursuers, (2) act cooperatively as a unified team of pursuers, and (3) act individually as greedy pursuers. The evader, on the other hand, will consider strategies against all possible strategies by the pursuers. We assume complete uncertainty in the game i.e. no player knows which strategies the other players are implementing and none of them has information about any of the parameters in the objective functions of the other players. To treat the three pursuers strategies under one general framework, an allagainstone linear quadratic dynamic game is considered and the corresponding closedloop Nash solution is discussed. Additionally, different necessary and sufficient conditions regarding the stability of the system, and existence and definiteness of the closedloop Nash strategies under different strategy assumptions are derived. We deal with the uncertainties in the strategies by first developing the Nash strategies for each of the resulting games for all possible options available to both sides. Then we deal with the parameter uncertainties by performing a Monte Carlo analysis to determine probabilities of capture for the pursuers (or escape for the evader) for each resulting game. Results of the Monte Carlo simulation show that in general, pursuers do not always benefit from cooperating as a team and that acting as noncooperating players may yield a higher probability of capturing of the evader.
Show less  Date Issued
 2017
 Identifier
 CFE0007135, ucf:52314
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0007135