On a Generalized Discrete Ratio-Dependent Predator-Prey System

Verifiable criteria are established for the permanence and existence of positive periodic solutions of a delayed discrete predator-prey model with monotonic functional response. It is shown that the conditions that ensure the permanence of this system are similar to those of its corresponding continuous system. And the investigations generalize some well-known results. In particular, a more acceptant method is given to study the bounded discrete systems rather than the comparison theorem

Contributions to mathematical analysis of non-linear models with applications in population dynamics

The PhD thesis deals with two research lines, both within the framework of mathematical analysis of non-linear models. The main differences appear in the type of equations we consider and the approach used. On the one hand, we give some extensions of fixed point results that improve the localization of solutions to boundary or initial value problems and we contribute to the application of fixed point theory to population models. On the other hand, our main aim is to describe the asymptotic dynamics and bifurcations of some discrete-time one-dimensional dynamical systems. We follow a more applied-oriented approach, dealing with some population models arising in fisheries management or blood cell production

Mathematical modeling of fall armyworm spodoptera frugiperda infestations in maize crops and its impact on final maize biomass

A Dissertation Submitted in Partial Fulfilment of the Requirements for the Degree of Doctor of Philosophy in Mathematical and Computer Sciences and Engineering of the Nelson Mandela African Institution of Science and TechnologyFall armyworm (FAW-Spodoptera frugiperda), a highly destructive and fast spreading agricul tural pest native to North and South America, poses a real threat to global food security. It is estimated that intermittent FAW outbreaks could cause up to $US 13 billion per annum in crop losses throughout sub-Saharan Africa. Considering this projected loss it is imperative that various tools and techniques be utilized to infer on the various factors that affect FAW maize in teraction and in-turn affect the final maize biomass. Mathematical modeling has proved to be an important tool that is capable of shedding light on the FAW-maize interaction dynamics. In this study, three mathematical models were proposed to evaluate the impact of memory effects and controls, seasonality and Integrated Pest Management strategy (farming awareness and larvae predation) on FAW infestations in maize crops and on final maize biomass. Firstly, to evaluate the impact of memory effects and control, a new dynamical system for FAW-maize biomass interaction via Caputo fractional-order operator was proposed and analyzed. In the proposed model, four equilibrium points which revealed the existence of a threshold parameter defined by R0 were computed and analyzed. Further, it was observed that, R0, the average number of newborns produced by one individual female moth during its life span was an integral compo nent for stability of the aforementioned model equilibria. Secondly, to evaluate the implications of seasonality on FAW maize interaction and on the final maize biomass, a non-autonomous mathematical model was proposed and analyzed. The analysis revealed that the model solution was non-negative, unique, permanent and bounded admitting global asymptotic and continuous periodic function. Further, the model was extended into an optimal control problem with the aim of determining optimal pesticides and traditional methods that are capable of minimizing FAW egg and larvae populations at minimum cost. Results from the study demonstrated that a combination of pesticides use at low intensity with traditional methods at higher intensity could eradicate FAW in a maize field in a period less than half the life span of the crop in the field. Thirdly, to evaluate the impact of farming awareness campaigns and larvae predation, a fractional-order model that incorporated farming awareness campaigns and larvae predation was proposed and analysed. Overall, the study highlighted that, non-time dependent farming awareness campaigns should be close to 100% all the time to eradicate the FAW. However, when time-dependent farming awareness was implemented, it was observed that even less than 50% intensity level could lead to eradication of FAW. In all the proposed models, comprehen sive numerical simulations were carried out in MATLAB programming language to support the analytical findings. In a nutshell, the results of this study showed that mathematical models can be important tools to evaluate FAW and maize interaction dynamics

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal