Applied Mathematics Commons^™

Modelling The Role Of Cloud Density On The Removal Of Gaseous Pollutants And Particulate Matters From The Atmosphere, Shyam Sundar, Rajan K. Sharma, Ram Naresh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a six dimensional nonlinear mathematical model is proposed to study the effect of the density of cloud droplets (formed due to the presence of vapors in the atmosphere) on the removal of pollutants, both gaseous and particulate, from the atmosphere. We assume that there exist six nonlinearly interacting phases in the atmosphere i.e. the vapor phase, the phase of cloud droplets, the phase of raindrops, the phase of gaseous pollutants, the phase of particulate matters and the phase of gaseous pollutants absorbed in raindrops. It is further assumed that the dynamics of the system undergo ecological type …

Exponentially Fitted Variants Of The Two-Step Adams-Bashforth Method For The Numerical Integration Of Initial Problems, Gurjinder Singh, V. Kanwar, Saurabh Bhatia

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we propose new variants of the two-step Adams-Bashforth and the one-step Adams-Moulton methods for the numerical integration of ordinary differential equations (ODEs). The methods are constructed geometrically from an exponentially fitted osculating parabola. The accuracy and stability of the proposed variants is discussed and their applicability to some initial value problems is also considered. Numerical experiments demonstrate that the exponentially fitted variants of the two-step Adams-Bashforth and the one-step Adams-Moulton methods outperform the existing classical two-step Adams-Bashforth and one-step Adams- Moulton methods respectively.

Mathematical Modeling And Analysis Of Asthma Stability And Severity, Arezoo Hanifi

Electronic Theses and Dissertations

Asthma is one of the most common chronic conditions in the United States. Asthma affects about one in fifteen people. It affects children more than adults and blacks more than whites. People with asthma experience attacks of wheezing, breathlessness, chest tightness, and coughing. Asthma can be fatal and the costs for the disease (direct and indirect) are approximated to be tens of billions of dollars each year.

There is no cure for asthma. However; for most people if asthma is controlled well they can lead normal, active lives. Therefore asthma controllability is a main factor in clinical practice. In order …

On Stability Of Dynamic Equations On Time Scales Via Dichotomic Maps, Veysel F. Hatipoğlu, Zeynep F. Koçak, Deniz Uçar

Applications and Applied Mathematics: An International Journal (AAM)

Dichotomic maps are used to check the stability of ordinary differential equations and difference equations. In this paper, this method is extended to dynamic equations on time scales; the stability and asymptotic stability to the trivial solution of the first order system of dynamic equations are examined using dichotomic and strictly dichotomic maps. This method, in dynamic equations, also involves Lyapunov’s direct method.

A Mathematical Study On The Dynamics Of An Eco-Epidemiological Model In The Presence Of Delay, T. K. Kar, Prasanta K. Mondal

Applications and Applied Mathematics: An International Journal (AAM)

In the present work a mathematical model of the prey-predator system with disease in the prey is proposed. The basic model is then modified by the introduction of time delay. The stability of the boundary and endemic equilibria are discussed. The stability and bifurcation analysis of the resulting delay differential equation model is studied and ranges of the delay inducing stability as well as the instability for the system are found. Using the normal form theory and center manifold argument, we derive the methodical formulae for determining the bifurcation direction and the stability of the bifurcating periodic solution. Some numerical …

Modeling And Analysis Of The Spread Of An Infectious Disease Cholera With Environmental Fluctuations, Manju Agarwal, Vinay Verma

Applications and Applied Mathematics: An International Journal (AAM)

A nonlinear delayed mathematical model with immigration for the spread of an infectious disease cholera with carriers in the environment is proposed and analyzed. It is assumed that all susceptible are affected by carrier population density. The carrier population density is assumed to follow the logistic model and grows due to conducive human population density related factors. The model is analyzed by stability theory of differential equations and computer simulation. Both the disease-free (DFE), (CFE) and endemic equilibria are found and their stability investigated. Bifurcation analyses about endemic equilibrium are also carried out analytically using the theory of differential equations. …

A Duhamel Integral Based Approach To Identify An Unknown Radiation Term In A Heat Equation With Non-Linear Boundary Condition, R. Pourgholi, M. Abtahi, A. Saeedi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider the determination of an unknown radiation term in the nonlinear boundary condition of a linear heat equation from an overspecified condition. First we study the existence and uniqueness of the solution via an auxiliary problem. Then a numerical method consisting of zeroth-, first-, and second-order Tikhonov regularization method to the matrix form of Duhamel's principle for solving the inverse heat conduction problem (IHCP) using temperature data containing significant noise is presented. The stability and accuracy of the scheme presented is evaluated by comparison with the Singular Value Decomposition (SVD) method. Some numerical experiments confirm the …

The Principle Of Linearized Stability For Size-Structured Population Models, M. El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

The principle of linearized stability for size-structured population dynamics models is proved giving validity to previous stability results reported in, for example, El-Doma (2008-1). In particular, we show that if all the roots of the characteristic equation lie to the left of the imaginary axis then the steady state is locally exponentially stable, and on the other hand, if there is at least one root that lies to the right of the imaginary axis then the steady state is unstable. We also point out cases when there is resonance

Stability Analysis And Application Of A Mathematical Cholera Model, Shu Liao, Jim Wang

Mathematics & Statistics Faculty Publications

In this paper, we conduct a dynamical analysis of the deterministic cholera model proposed in [9]. We study the stability of both the disease-free and endemic equilibria so as to explore the complex epidemic and endemic dynamics of the disease. We demonstrate a real-world application of this model by investigating the recent cholera outbreak in Zimbabwe. Meanwhile, we present numerical simulation results to verify the analytical predictions.

New Computational Algorithms For Analyzing The Stability Of The Differential Equations System, H. S. Najafi, A. H. Refahi Sheikhani

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we show how to improve the approximate solution of the large Lyapunov equation obtained by an arbitrary method. Moreover, we propose a new method based on refinement process and Weighted Arnoldi algorithm for solving large Lyapunov matrix equation. Finally, some numerical results will be reported to illustrate the efficiency of the proposed method.

Asymptotic Expansions And Stability Of Hybrid Systems With Two-Time Scales, Dung Tien Nguyen

Wayne State University Dissertations

In this dissertation, we consider solutions of hybrid systems in which both continuous dynamics and discrete events coexists. One

of the main ingredients of our models is the two-time-scale formulation. Under broad conditions, asymptotic expansions are developed for the solutions of the systems of backward equations for switching diffusion in two classes of models, namely, fast switching systems and fast diffusion systems. To prove the validity of the asymptotic expansions, uniform error bounds are obtained.

In the second part of the dissertation, a singular linear system is considered. Again a two-time-scale formulation is used. Under suitable conditions, the system has …

Interaction Of Excited States In Two-Species Bose-Einstein Condensates: A Case Study, Todd Kapitula, Kody J. H. Law, Panayotis G. Kevrekidis

University Faculty Publications and Creative Works

In this paper we consider the existence and spectral stability of excited states in two-species Bose-Einstein condensates in the case of a pancake magnetic trap. Each new excited state found in this paper is to leading order a linear combination of two one-species dipoles, each of which is a spectrally stable excited state for one-species condensates. The analysis is done via a Lyapunov-Schmidt reduction and is valid in the limit of weak nonlinear interactions. Some conclusions, however, can be made at this limit which remain true even when the interactions are large.

Mathematical Models And Stability Analysis Of Cholera Dynamics, Shu Liao

Mathematics & Statistics Theses & Dissertations

In this dissertation, we present a careful mathematical study of several epidemic cholera models, including the model of Codeco [11] in 2001, that of Hartley, Morris and Smith [22] in 2006, and that of Mukandavire, Liao, Wang and Gaff et al. [60] in 2010. We formally derive the basic reproduction number R0 for each model by computing the spectral radius of the next generation matrix. We focus our attention on the stability analysis at the disease-free equilibrium which determines the short-term epidemic behavior, and the endemic equilibrium which determines the long-term disease dynamics. Particularly, we incorporate the Volterra-Lyapunov matrix …

Forced Oscillations Of The Korteweg-De Vries Equation On A Bounded Domain And Their Stability, Muhammad Usman, Bingyu Zhang

Mathematics Faculty Publications

It has been observed in laboratory experiments that when nonlinear dispersive waves are forced periodically from one end of undisturbed stretch of the medium of propagation, the signal eventually becomes temporally periodic at each spatial point. The observation has been confirmed mathematically in the context of the damped Kortewg-de Vries (KdV) equation and the damped Benjamin-Bona-Mahony (BBM) equation. In this paper we intend to show the same results hold for the pure KdV equation (without the damping terms) posed on a bounded domain. Consideration is given to the initial-boundary-value problem

uu_xu_xxx 0 < x < 1, t > 0, (*)

It is shown …

Remarks On The Stability Of Some Size-Structured Population Models V: The Case When The Death Rate Depends On Adults Only And The Growth Rate Depends On Size Only, M. El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

We continue our study of size-structured population dynamics models when the population is divided into adults and juveniles, started in El-Doma (To appear). We concentrate our efforts in the special case when the death rate depends on adults only, the growth rate depends on size only and the maximum size for an individual in the population is infinite. Three demographic parameters are identified and are shown to determine conditions for the (in)stability of a nontrivial steady state. We also give examples that illustrate the stability results. The results in this paper generalize previous results, for example, see Calsina, et al. …

Remarks On The Stability Of Some Size-Structured Population Models Iv: The General Case Of Juveniles And Adults, M. El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

The stability of some size-structured population dynamics models is investigated when the population is divided into adults and juveniles. We determine the steady states and study their stability. We also give examples that illustrate the stability results. The results in this paper generalize previous results, for example, see Calsina, et al. (2003), El-Doma (2006), Farkas, et al. (2008), and El-Doma (2008 a).

Remarks On The Stability Of Some Size-Structured Population Models Vi: The Case When The Death Rate Depends On Juveniles Only And The Growth Rate Depends On Size Only And The Case When Both Rates Depend On Size Only, M. El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

We continue our study of size-structured population dynamics models when the population is divided into adults and juveniles, started in El-Doma (to appear 1) and continued in El-Doma (to appear 2). We concentrate our efforts in two special cases, the first is when the death rate depends on juveniles only and the growth rate depends on size only, and, the second is when both the death rate and the growth rate depend on size only. In both special cases we assume that the maximum size for an individual in the population is infinite. We identify three demographic parameters and show …

Stability Of An Age-Structured Seir Epidemic Model With Infectivity In Latent Period, Xue-Zhi Li, Bin Fang

Applications and Applied Mathematics: An International Journal (AAM)

We study an age-structured SEIR epidemic model with infectivity in the latent period. By using the theory and methods of Differential and Integral Equations, the explicit expression for the basic reproductive number R₀ is first derived. It is shown that the disease-free equilibrium is locally and globally asymptotically stable if R₀ < 1. It is then proved that only one endemic equilibrium exists if R₀ > 1 and its stability conditions are also given.

Bifurcation Analysis Of A Kaldor-Kalecki Model Of Business Cycle With Time Delay, Liancheng Wang, Xiaoqin P. Wu

Faculty Articles

In this paper, we investigate a Kaldor-Kalecki model of business cycle with delay in both the gross product and the capital stock. Stability analysis for the equilibrium point is carried out. We show that Hopf bifurcation occurs and periodic solutions emerge as the delay crosses some critical values. By deriving the normal forms for the system, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established. Examples are presented to confirm our results.

Remarks On The Stability Of Some Size-Structured Population Models Iii: The Case Of Constant Inflow Of Newborns, Mohammed El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

The stability of some size-structured population dynamics models are investigated. We determine the steady states and study their stability. We also give examples that illustrate the stability results. The results in this paper generalize previous results, for example, see Calsina, et al. (2003), El- Doma (2006) and El-Doma (2008).

Remarks On The Stability Of Some Size-Structured Population Models Ii: Changes In Vital Rates Due To Size And Population Size, Mohammed El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

The stability of some size-structured population dynamics models are investigated. We determine the steady states and study their stability. We also give examples that illustrate the stability results. The results in this paper generalize previous results, for example, see Calsina, et al. (2003) and El-Doma (2006).

Mathematical Analysis Of The Transmission Dynamics Of Hiv/Tb Coinfection In The Presence Of Treatment, Oluwaseun Sharomi, Chandra N. Podder, Abba B. Gumel, Baojun Song

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

This paper addresses the synergistic interaction between HIV and mycobacterium tuberculosis using a deterministic model, which incorporates many of the essential biological and epidemiological features of the two diseases. In the absence of TB infection, the model (IIIV-only model) is shown to have a globally asymptotically stable, disease-free equilibrium whenever the associated reproduction number is less than unity and has a unique endemic equilibrium whenever this number exceeds unity. On the other hand, the model with TB alone (TB-only model) undergoes the phenomenon of backward bifurcation, where the stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated …

Age-Structured Population Model With Cannibalism, Mmohammed El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

An age-structured population model with cannibalism is investigated. We determine the steady states and study the local asymptotic stability as well as the global stability. The results in this paper generalize previous results.

Stability Analysis For The Gurtin-Maccamy’S Age-Structured Population Dynamics Model, Mohammed El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

The stability of the Gurtin-MacCamy’s age-structured population dynamics model is investigated. We determine the steady states and study their stability. The results in this paper generalize previous results.

Stability Analysis For An Seir Age-Structured Epidemic Model Under Vaccination, M. El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

An SEIR age-structured epidemic model is investigated when susceptible and immune individuals are vaccinated indiscriminately and the force of infection of proportionate mixing type. We determine the steady states and obtain an explicitly computable threshold condition, and then study the stability of the steady states.

Investigation Of The Stability Of Engine – Governor System Operated At Low Speeds, Cuthbert Mhilu

Tanzania Journal of Engineering and Technology (TJET)

During diesel engine operation, a tendency for the engine not to achieve a  steady idling speed has often been observed. During idling speed the engine tends to either race or stall as a result of poor and incorrect metering of the fuel, which is required for the combustion process and if severe, the engine will stop firing completely. 111 this research an investigation was made to establish knowledge on diesel engine stability operated at low speeds. The influence of a governor of an engine in the control of the engine speeds has also been investigated. In order to obtain information …

Analysis Of An Sirs Age-Structured Epidemic Model With Vaccination And Vertical Transmission Of Disease, Mohammed El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

An SIRS age-structured epidemic model for a vertically as well as horizontally transmitted disease under vaccination is investigated when the fertility, mortality and removal rates depend on age and the force of infection of proportionate mixing assumption type, and vaccination wanes over time. We prove the existence and uniqueness of solution to the model equations, and show that solutions of the model equations depend continuously on the initial age-distributions. Furthermore, we determine the steady states and obtain an explicitly computable threshold condition, in terms of the demographic and epidemiological parameters of the model; we then study the stability of the …

Remarks On The Stability Of Some Size-Structured Population Models I: Changes In Vital Rates Due To Population Only, Mohammed El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

We consider a size-structured population model that has been studied in Calsina et al. (2003). We propose a different approach that provides direct stability results, and we correct a stability result given therein. In addition, we obtain global stability results that have not been given in Calsina et al. (2003).

The Asymptotics Of Neutral Curve Crossing In Taylor–Dean Flow, C. P. Hills, A. P. Bassom

Articles

The fluid flow between a pair of coaxial circular cylinders generated by the uniform rotation of the inner cylinder and an azimuthal pressure gradient is susceptible to both Taylor and Dean type instabilities. The flow can be characterised by two parameters: a measure of the relative magnitude of the rotation and pressure effects and a non-dimensional Taylor number. This work considers the small gap, large wavenumber limit for linear perturbations when the onset of the Taylor and Dean instabilities is concurrent. A consistent, matched asymptotic solution is found across the whole annular domain and identifies five regions of interest: two …

Stability In Dynamical Polysystems, George Cazacu

LSU Doctoral Dissertations

A dynamical polysystem consists of a family of continuous dynamical systems, all acting on a given metric space. The first chapter of the present thesis shows a generalization of control systems via dynamical polysystems and establishes the equivalence of the two notions under certain lipschitz condition on the function defining the dynamics. The remaining chapters are focused on a basic theory of dynamical polysystems. Some topological properties of limit sets are described in Chapter 2. Chapters 3 and 4 provide characterizations for various notions of strong stability. Chapter 5 makes use of the theory of closed relations to study Lyapunov …