Diss.--Math.--Berlin--Freie Universität, 1997. / Bibliogr. p. 86-90.

Thèse de doctorat : Automatique, traitement du signal et des images : Nice : 2005. / Bibliogr. p. 229-238. Résumés en français et en anglais.

No description available.

In this thesis we consider new approaches to the numerical solution of a class of Volterra integral equations, which contain a kernel with singularity of non-standard type. The kernel is singular in both arguments at the origin, resulting in multiple solutions, one of which is differentiable at the origin. We consider numerical methods to approximate any of the (infinitely many) solutions of the equation. We go on to show that the use of product integration over a short primary interval, combined with the careful use of extrapolation to improve the order, may be linked to any suitable standard method away from the origin. The resulting split-interval algorithm is shown to be reliable and flexible, capable of achieving good accuracy, with convergence to the one particular smooth solution.

Thesis (M.App.Sc.) - Carleton University, 2007. / Includes bibliographical references (p. 49-50). Also available in electronic format on the Internet.

Thesis (M.Eng.)(Control)--University of Pretoria, 2004. / Summaries in English and Afrikaans. Includes bibliographical references.

The control of flotation circuits is a complicated problem, since flotation circuits are nonlinear multivariable processes with a significant degree of interaction between the variables. Isolated PID controllers usually do not perform adequately. The application of a nonlinear model predictive algorithm based on second order Volterra models was investigated. Volterra series models are a higher order extension of linear impulse response models. The nonlinear model predictive control algorithm can also be seen as a linear model predictive controller with higher order correction terms. A dynamic model of a flotation circuit based on the governing continuity equations was developed. The responses obtained represented the qualitative relationships between the model inputs and the controlled variables. This model exhibited strong nonlinearities, including asymmetrical responses to symmetrical inputs and gain sign changes. This dynamic model was treated as the plant to be identified and from which second order Volterra models were obtained. Full Volterra models required excessively large data sets, but significant reductions in the size of the required data set could be achieved if some of the second order coefficients were constrained to zero. These "pruned" Volterra models represented the plant dynamics significantly better than linear models. In particular, these second order Volterra models were able to model asymmetrical responses including gain sign changes. A special case of "pruned" second order Volterra models are diagonal second order models, where all the off-diagonal coefficients (hij where i ≠ j) are constrained to zero. These models required less data than pruned Volterra models containing off-diagonal coefficients, but were less accurate. The performance of nonlinear model predictive controllers based on a pruned second order and diagonal second order Volterra models was evaluated. The performance of these controllers was also compared to the performance obtained with a first order (linear) Volterra model. All three controllers gave equivalent results for large manipulated variable weights. However, when the controllers were tuned more aggressively, results obtained from the three controllers differed considerably. The pruned nonlinear controller performed well even when tuned aggressively while the performance of the linear controller deteriorated. For the case of disturbance rejection, the linear controller performed slightly better than the nonlinear controllers. / Dissertation (MEng (Control Engineering))--University of Pretoria, 2006. / Chemical Engineering / unrestricted

<p> This thesis studies the optical and electronic compensation for fiber nonlinearities based on the theory of Volterra expression. Signals propagating through optical fibers suffer from both linear and nonlinear distortion. In this thesis, we first construct an approximate inverse of fiber systems based on the theory of pth-order inverse of Volterra expansion. For a fully dispersion compensated fiber system H with a second-order dispersion profile f32 (z) and a total length of L, if the input field is real, we show that the inverse can be approximated by a system K with an inverted seconder-order dispersion profile -/32 ( z-L), while keeping all the other parameters the same. We then further develop the scheme by adding an optical phase conjugator ( OPC) in the middle of the transmission line. More specifically, the inversion of a fully dispersion compensated N-span fiber system H with a second-order dispersion profile /32 (z) and a total length L, is realized using an OPC followed by another N-span system K with an inverted seconder-order dispersion profile -f32(z-L), while keeping all the other parameters the same. In this way the original input optical signals can be recovered exactly. Our analytical and numerical simulation results show that the scheme works well for both single-channel systems and WDM systems. For electronic compensation techniques, we examine a nonlinear intersymbol interference (ISI) canceler based on Volterra theory, which was proposed first for voiceband data transmission, and apply it to optical fiber systems here, for the first time to our knowledge. The canceler is able to compensate nonlinear ISI caused by the cross product of both precursor and post cursor. </p> / Thesis / Master of Applied Science (MASc)

In a stochastic Lotka-Volterra model on a two-dimensional square lattice with periodic boundary conditions and subject to occupation restrictions, there exists an extinction threshold for the predator population that separates a stable active two-species coexistence phase from an inactive state wherein only prey survive. When investigating the non-equilibrium relaxation of the predator density in the vicinity of the phase transition point, we observe critical slowing-down and algebraic decay of the predator density at the extinction critical point. The numerically determined critical exponents are in accord with the established values of the directed percolation universality class. Following a sudden predation rate change to its critical value, one finds critical aging for the predator density autocorrelation function that is also governed by universal scaling exponents. This aging scaling signature of the active-to-absorbing state phase transition emerges at significantly earlier times than the stationary critical power laws, and could thus serve as an advanced indicator of the (predator) population's proximity to its extinction threshold. In order to study boundary effects, we split the system into two patches: Upon setting the predation rates at two distinct values, one half of the system resides in an absorbing state where only the prey survives, while the other half attains a stable coexistence state wherein both species remain active. At the domain boundary, we observe a marked enhancement of the predator population density, the minimum value of the correlation length, and the maximum attenuation rate. Boundary effects become less prominent as the system is successively divided into subdomains in a checkerboard pattern, with two different reaction rates assigned to neighboring patches. We furthermore add another predator species into the system with the purpose of studying possible origins of biodiversity. Predators are characterized with individual predation efficiencies and death rates, to which "Darwinian" evolutionary adaptation is introduced. We find that direct competition between predator species and character displacement together play an important role in yielding stable communities. We develop another variant of the lattice predator-prey model to help understand the killer- prey relationship of two different types of E. coli in a biological experiment, wherein the prey colonies disperse all over the plate while the killer cell population resides at the center, and a "kill zone" of prey forms immediately surrounding the killer, beyond which the prey population gradually increases outward. / Ph. D. / We utilize Monte-Carlo simulations to study population dynamics of Lotka–Volterra model and its variants. Our research topics include the non-equilibrium phase transition from a predator-prey coexistence state to an absorbing state wherein only prey survive, boundary effects in a spatially inhomogeneous system, the stabilization of a three species system with direct competition and “Darwinian” evolutionary adaption introduced, and the formation of spatial patterns in a biological experiment of two killer and prey E. coli species.

Made available in DSpace on 2014-08-13T14:50:57Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-02-21Bitstream added on 2014-08-13T17:59:56Z : No. of bitstreams: 1 000768672.pdf: 713902 bytes, checksum: bffc0a4e01880e1ffdb1dcb96c2a05b6 (MD5) / Este trabalho trata do Cálculo Fracionário e suas aplicações em problemas biológicos. Nas aplicações nos concentramos no sistema de Lotka-Volterra clássico e fracionário, para depois analisar o controle biológico da praga da cana-de-açúcar. Como trabalho futuro, propomos analisar as aplicações do sistema de Lotka-Volterra fracionário em problemas reais do câncer, com saturação de crescimento tumoral enfocando tratamento quimioterápico / This work is about Fractional Calculus and its applications in biological problems. In the applications we focus on the classical Lotka-Volterra system and into the corresponding fractional order version to examine the biological control of sugar cane’s pest. As future work, we analyze the fractional system in real problems of cancer, with saturation of tumor growth with a focus on chemotherapy