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.

This research was done to study the effect of sea severity on the vertical ship responses like heave and pitch. Model testing of a 175m moored container ship with zero heading speed was done for different sea states varying from very rough to very high seas. Transfer functions were extracted using Volterra model which constitutes both linear and quadratic part. The experimental linear transfer functions were calculated using Volterra linear model and were compared with linear transfer function from the hydrodynamic theory. Experimental second order transfer functions were also extracted using Volterra quadratic model and their behavior was studied for different sea states. After the extraction of linear and second order transfer functions total responses were reconstructed and compared with the measured responses. This also helped to investigate the contribution of second order part to the total vertical ship responses. In the last stage of the research a new semi- empirical method was developed called as ‘UNIOM’ for the prediction of the responses. Laboratory input waves and theoretical LTFs were used for the simulation of ship response and these were compared with measured responses.

We study diffusion-reaction-advection models describing population dynamics of aquatic organisms subject to a constant drift, with reflecting upstream and outflow downstream boundary conditions. We consider three different models: single logistically growing species, two and three competing species. In the case of a single population, we determine conditions for existence, uniqueness and stability of non-trivial steady-state solutions. We analyze the dependence of such solutions on advection speed, growth rate and length of the habitat. Such analysis offers a possible explanation of the "drift paradox" in our context. We also introduce a spatially implicit ODE (nonspatial approximation) model which captures the essential behavior of the original PDE model. In the case of two competing species, we use a diffusion-advection version of the Lotka-Volterra competition model. Combining numerical and analytical techniques, in both the spatial and nonspatial approximation settings, we describe the effect of advection on competitive outcomes. Finally, in the case of three species, we use the nonspatial approximation approach to analyze and classify the possible scenarios as we change the flow speed in the habitat.

We study diffusion-reaction-advection models describing population dynamics of aquatic organisms subject to a constant drift, with reflecting upstream and outflow downstream boundary conditions. We consider three different models: single logistically growing species, two and three competing species. In the case of a single population, we determine conditions for existence, uniqueness and stability of non-trivial steady-state solutions. We analyze the dependence of such solutions on advection speed, growth rate and length of the habitat. Such analysis offers a possible explanation of the "drift paradox" in our context. We also introduce a spatially implicit ODE (nonspatial approximation) model which captures the essential behavior of the original PDE model. In the case of two competing species, we use a diffusion-advection version of the Lotka-Volterra competition model. Combining numerical and analytical techniques, in both the spatial and nonspatial approximation settings, we describe the effect of advection on competitive outcomes. Finally, in the case of three species, we use the nonspatial approximation approach to analyze and classify the possible scenarios as we change the flow speed in the habitat.

This study presents the results of an extraction of the 2nd-order nonlinear responses from model test data. Emphasis is given on the effects of assumptions made for the Gaussian and non-Gaussian input on the estimation of the 2nd-order response, employing the quadratic Volterra model. The effects of sea severity and data length on the estimation of response are also investigated at the same time. The data sets used in this study are surge forces on a fixed barge, a surge motion of a compliant mini TLP (Tension Leg Platform), and surge forces on a fixed and truncated column. Sea states are used from rough sea (Hs=3m) to high sea (Hs=9m) for a barge case, very rough sea (Hs=3.9m) for a mini TLP, and phenomenal sea (Hs=15m) for a truncated column. After the estimation of the response functions, the outputs are reconstructed and the 2nd order nonlinear responses are extracted with all the QTF distributed in the entire bifrequency domain. The reconstituted time series are compared with the experiment in both the time and frequency domains. For the effects of data length on the estimation of the response functions, 3, 15, and 40- hour data were investigated for a barge, but 3-hour data was used for a mini TLP and a fixed and truncated column due to lack of long data. The effects of sea severity on the estimation of the response functions are found in both methods. The non-Gaussian method for estimation is more affected by data length than the Gaussian method.

We study diffusion-reaction-advection models describing population dynamics of aquatic organisms subject to a constant drift, with reflecting upstream and outflow downstream boundary conditions. We consider three different models: single logistically growing species, two and three competing species. In the case of a single population, we determine conditions for existence, uniqueness and stability of non-trivial steady-state solutions. We analyze the dependence of such solutions on advection speed, growth rate and length of the habitat. Such analysis offers a possible explanation of the "drift paradox" in our context. We also introduce a spatially implicit ODE (nonspatial approximation) model which captures the essential behavior of the original PDE model. In the case of two competing species, we use a diffusion-advection version of the Lotka-Volterra competition model. Combining numerical and analytical techniques, in both the spatial and nonspatial approximation settings, we describe the effect of advection on competitive outcomes. Finally, in the case of three species, we use the nonspatial approximation approach to analyze and classify the possible scenarios as we change the flow speed in the habitat.

Abstract The main emphasis in modern RF power amplifier (PA) research is on improving linearity while at the same time maintaining reasonably good efficiency, for which purpose external linearization in the form of feedforward or predistortion is often used. Linearity and linearization can be considered from both a fundamental signal (amplitude and phase conversions, AM-AM & AM-PM) and an intermodulation distortion (IMD) regeneration point of view, and since a study of intermodulation gives more information on the behaviour of an amplifier, linearity is studied in this thesis by analysing the amplitude and phase of IM components under varying signal conditions, i.e. as functions of temperature, modulation bandwidth and amplitude. To study the behaviour of IM components analytically, a Volterra model including electro-thermal distortion mechanisms is developed and a simulation technique is introduced to determine how easily the amplifier can be linearized. An S-parameter characterization method for extracting the Volterra model and the simulation model is developed, and the amplitude and phase dependences of the IM components are shown by means of measurements performed by a novel technique developed here. The results show that the behaviour of IM components is more complicated than had commonly been expected. Three techniques are developed for eliminating the frequency dependence of IM components, impedance optimization, envelope filtering and envelope injection. In the envelope injection technique, a low frequency envelope signal is added to the input of the amplifier in order to improve both the bandwidth and amplitude range of the memoryless predistortion. The functionality of envelope injection is demonstrated by Volterra calculations, simulations and measurements, and the technique is applied to 1W, 1.8 GHz common-emitter BJT and common-source MESFET amplifiers. IM cancellation better than 20 dB is achieved over a wide range of bandwidths and amplitudes. It is concluded that an inherently linear amplifier is not necessarily easy to linearize any further using external techniques, but that the part of the distortion that varies with bandwidth and amplitude can be cancelled out using envelope injection and the remaining memoryless distortion by means of a simple polynomial RF predistorter. This results in good cancellation of distortion, and since both envelope injection and RF predistortion consume little power, both good efficiency and linearity can be achieved.

We study diffusion-reaction-advection models describing population dynamics of aquatic organisms subject to a constant drift, with reflecting upstream and outflow downstream boundary conditions. We consider three different models: single logistically growing species, two and three competing species. In the case of a single population, we determine conditions for existence, uniqueness and stability of non-trivial steady-state solutions. We analyze the dependence of such solutions on advection speed, growth rate and length of the habitat. Such analysis offers a possible explanation of the "drift paradox" in our context. We also introduce a spatially implicit ODE (nonspatial approximation) model which captures the essential behavior of the original PDE model. In the case of two competing species, we use a diffusion-advection version of the Lotka-Volterra competition model. Combining numerical and analytical techniques, in both the spatial and nonspatial approximation settings, we describe the effect of advection on competitive outcomes. Finally, in the case of three species, we use the nonspatial approximation approach to analyze and classify the possible scenarios as we change the flow speed in the habitat.

Orientador: Prof. Dr. Roberto Venegeroles Nascimento / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, 2016. / Neste trabalho se estudaram aspectos básicos relacionados com a dinâmica de células cancerígenas do tipo B-Linfoma BCL1 e de gliomas fazendo ênfases neste último caso. O trabalho se iniciou revisando alguns modelos populacionais do câncer inspirados nos trabalhos de Lotka e Volterra o qual oferecem uma descrição muito simples da interação entre o câncer (presa) e o sistema imunológico (caçador). Posteriormente é revisado um modelo global espaço-temporal baseado nas equações de Fisher-Kolmogorov-Petrovsky- Piskounov (FKPP) [1] o qual permitiu aclarar a dicotomia entre proliferação e motilidade associada fortemente ao crescimento tumoral e à invasividade, respectivamente, das células cancerosas. A partir do modelo FKPP também se fez um estudo computacional mais detalhado aplicando diferentes protocolos de tratamentos para analisar seus efeitos sobre o crescimento e desenvolvimento de gliomas. O estudo sugere que um tratamento com maior tempo entre cada dose poderia ser mais ótimo do que um tratamento mais agressivo. Propõe-se também um modelo populacional local do câncer em que se tem em conta o caráter policlonal das células cancerígenas e as interações destas com o sistema imunológico natural e especifico. Neste último modelo se consegui apreciar fenômenos como dormancy state (estado de latência) e escape phase (fase de escape) para valores dos parâmetros correspondentes ao câncer de tipo B-Linfoma BCL1 [2] o qual explica os fenômenos de imunoedição e escape da imunovigilância [3] o qual poderia permitir propor novos protocolos de tratamentos mais apropriados.Depois se fez uma reparametrização do modelo baseado em algumas características mais próprias das células tumorais do tipo glioma e assumindo presença de imunodeficiência com o que se obtém coexistências oscilatórias periódicas tanto da população tumoral assim como das células do sistema imunológico o qual poderia explicar os casos clínicos de remissão e posterior reincidência tumoral. Finalmente se obtiveram baixo certas condições, uma dinâmica caótica na população tumoral o qual poderia explicar os casos clínicos em que se apresentam falta de controlabilidade da doença sobre tudo em pessoas idosas ou com algum quadro clinico que envolve alguma deficiência no funcionamento normal do sistema imunológico. / In this work we studied basic aspects of the dynamics of cancer cell type B-Lymphoma BCL1 and gliomas making strong emphasis in the latter case. We start reviewing some population models of cancer inspired in the work¿s of Lotka and Volterra, which offers a very simple description of the interaction between cancer (prey) and the immune system (Hunter). Subsequently revise a global model space-time based on the equations of Fisher-Kolmogorov-Petrovsky-Piskounov (FKPP) [1] which allowed elucidating the dichotomy between proliferation and strongly associated motility to tumor growth and invasiveness, respectively, of cancer cells. From the FKPP model also made a more detailed computer study applying different treatment protocols to analyze their effects on the growth and development of gliomas. The study suggests that treatment with longer time between each dose could be more optimal than a more aggressive treatment. Is studied also a local population cancer model that takes into account the polyclonal nature of cancer cells, and these interactions with the natural and specific immune system. In the latter model is able to appreciate phenomena as dormancy state and escape phase for values of parameters corresponding to lymphoma cancer BCL1 [2] which explains the phenomena of immunoediting and tumor escape immuno-surveillance [3] allowing elucidating treatments protocols more appropriate. A re-parameterization was made based on some features of tumor cells glioma type and assuming presence of immunodeficiency with that obtained coexistences periodic oscillatory both tumor populations as well as the immune system cells which could explain the clinical cases of remission and subsequent tumor recurrence. Finally obtained under certain conditions, a chaotic dynamics in tumor population which could explain the clinical cases that present lack of controllability of the disease on all in elderly or with some clinical picture involving some deficiency in the normal functioning of the immune system.

The thesis describes various modifications of the predator-prey model. The modifications are considering several harvesting methods. At the beginning a solution and a sensitivity analysis of the basic model are provided. The first modification is the percentage harvesting model, which could be easily converted to the basic model. Secondly a constant harvesting including a linearization is derived. A significant part is devoted to regulation models with special a focus on environmental applications and the stability of the system. Optimization algorithms for one and both species harvesting are derived and back-tested. One species harvesting is based on econometrical tools; the core of two species harvesting is the modified Newton's method. The economic applications of the model in macroeconomics and oligopoly theory are expanded using the methods derived in the thesis.