Parametric excitation and dispersal are added to discrete-time population models. Discrete-time models for growth with dispersal share many of the attributes of reaction-diffusion equations. At the same time, these models readily exhibit period doubling and chaos. Large parametric excitation (seasonality) is inevitably destabilizing, but mild seasonality may have a pronounced stabilizing effect. Seasonality also allows for the coexistence of alternative stable states (equilibria, cycles, chaos). Many examples are presented.

We address the problem of the consistency between discrete and continuous models for density-dependent size-structured populations. Some earlier works have discussed the consistency of density independent age and size-structured models. Although the issue of consistency between these models has raised interest in recent years, it has not been discussed in depth, perhaps because of the non-linear nature of the equations involved. We construct a numerical scheme of the continuous model and show that the transition matrix of this scheme has the form of the standard discrete model. The construction is based on the theory of Upwind Numerical Schemes for non-Linear Hyperbolic Conservation Laws with one important difference, that we do have a non-linear source at the boundary; interestingly, this case has not been explored in depth from the purely mathematical point of view. We prove the consistency, non-linear stability and hence convergence of the numerical scheme which guarantee that both models yield results that are completely consistent with each other. Several examples are worked out: a simple linear age-structured problem, a density-independent size-structured problem and a non-linear size-structured problem. These examples confirm the convergence just proven theoretically. An ample revision of relevant biological and computational literature is also presented and used to establish realistic restrictions on the objects under consideration and to prepare significant examples to illustrate our points.

The current state of information concerning the classical model of deterministic, age-dependent population dynamics - the McKendrick von Foerster equation - is overviewed. This model and the related Renewal equation are derived and the parameters involved in both are elaborated upon. Fundamental theorems concerning existence, uniqueness and boundedness of solutions are outlined. A necessary and sufficient condition concerning the stability of equilibrium age-distributions is rederived along different lines. Attention is then given to generalizations of the McKendrick-von Foerster model that have arisen from the inclusion of density- dependence into the parameters of the system; the inclusion of harvesting terms; and the extension of the model to describe the dynamics of a two-sex population. A technique which reduces the model, under certain conditions on the mortality and fertility functions, to a system of ordinary differential equations is discussed and applied to specific biochemical population models. Emphasis here is on the possible existence of stable limit cycles.The Kolmogorov system of ordinary differential equations and its use in describing the dynamics of predator-prey systems is examined. The Kolmogorov theorem is applied as a simple alternative to a lengthy algorithm for determining whether limit cycles are stable. Age-dependence is incorporated into this system by means of a McKendrick - von Foerster equation and the effects on the system of different patterns of age-selective predation are demonstrated. Finally, brief mention is made of recent work concerning the use of the McKendrick - von Foerster equation to describe the dynamics of both predator and prey. A synthesis of the theory and results of a large number of papers is sought and areas valuable to further research are pointed out. / Thesis (M.Sc.)-University of Natal, Durban, 1988.

Guo Bao Zhu. / Thesis (Ph.D.)--Chinese University of Hong Kong. / Includes bibliographical references. / Abstract --- p.1 / Introduction --- p.3 / Chapter Chapter 1. --- Semigroup for Age-Dependent Population Equations with Time Delay / Chapter 1.1 --- Introduction --- p.13 / Chapter 1.2 --- Problem Statement and Linear Theory --- p.14 / Chapter 1.3 --- Spectral Properties of the Infinitesimal Generator --- p.20 / Chapter 1.4 --- A Nonlinear Semigroup of the Logistic Age-Dependent Model with Delay --- p.26 / References --- p.34 / Chapter Chapter 2. --- Global Behaviour of Logistic Model of Age-Dependent Population Growth / Chapter 2.1 --- Introduction --- p.35 / Chapter 2.2 --- Global Behaviour of the Solutions --- p.37 / Chapter 2.3 --- Oscillatory Properties --- p.47 / References --- p.51 / Chapter Chapter 3. --- Semigroups for Age-Size Dependent Population Equations with Spatial Diffusion / Chapter 3. 1 --- Introduction --- p.52 / Chapter 3.2 --- Properties of the Infinitesimal Generator --- p.54 / Chapter 3.3 --- Properties of the Semigroup --- p.59 / Chapter 3.4 --- Dynamics with Age-Size Structures --- p.61 / Chapter 3.5 --- Logistic Model with Diffusion --- p.66 / References --- p.70 / Chapter Chapter 4. --- Semi-Discrete Population Equations with Time Delay / Chapter 4. 1 --- Introduction --- p.72 / Chapter 4.2 --- Linear Semi-Discrete Model with Time Delay --- p.74 / Chapter 4.3 --- Nonlinear Semi-Discrete Model with Time Delay --- p.88 / References --- p.98 / Chapter Chapter 5. --- A Finite Difference Scheme for the Equations of Population Dynamics / Chapter 5.1 --- Introduction --- p.99 / Chapter 5.2 --- The Discrete System --- p.102 / Chapter 5.3 --- The Main Results --- p.107 / Chapter 5.4 --- A Finite Difference Scheme for Logistic Population Model --- p.113 / Chapter 5.5 --- Numerical Simulation --- p.116 / References --- p.119 / Chapter Chapter 6. --- Optimal Birth Control Policies I / Chapter 6. 1 --- Introduction --- p.120 / Chapter 6.2 --- Fixed Horizon and Free Point Problem --- p.120 / Chapter 6.3 --- Time Optimal Control Problem --- p.129 / Chapter 6.4 --- Infinite Horizon Problem --- p.130 / Chapter 6.5 --- Results of the Nonlinear System with Logistic Term --- p.143 / Reference --- p.148 / Chapter Chapter 7. --- Optimal Birth Control Policies II / Chapter 7. 1 --- Free Final Time Problems --- p.149 / Chapter 7.2 --- Systems with Phase Constraints --- p.160 / Chapter 7.3 --- Mini-Max Problems --- p.166 / References --- p.168 / Chapter Chapter 8. --- Perato Optimal Birth Control Policies / Chapter 8.1 --- Introduction --- p.169 / Chapter 8.2 --- The Duboviskii-Mi1yutin Theorem --- p.171 / Chapter 8.3 --- Week Pareto Minimum Principle --- p.172 / Chapter 8.4 --- Problem with Nonsmooth Criteria --- p.175 / References --- p.181 / Chapter Chapter 9. --- Overtaking Optimal Control Problems with Infinite Horizon / Chapter 9. 1 --- Introduction --- p.182 / Chapter 9.2 --- Problem Statement --- p.183 / Chapter 9.3 --- The Turnpike Property --- p.190 / Chapter 9.4 --- Existence of Overtaking Optimal Solutions --- p.196 / References --- p.198 / Chapter Chapter 10. --- Viable Control in Logistic Populatiuon Model / Chapter 10. 1 --- Introduction --- p.199 / Chapter 10. 2 --- Viable Control --- p.200 / Chapter 10.3 --- Minimum Time Problem --- p.205 / References --- p.208 / Author's Publications During the Candidature --- p.209

We study problems in the stability of nonlinear ecological models and in the theory of collective motion in physical systems. We first establish criteria for global stability in deterministic nonlinear population models, including the most general criteria so far available for the Lotka-Volterra model. Next we study conditions for coexistence under periodic perturbations in population models and establish criteria for the appearance of dynamic equilibrium states. The third study in ecological stability establishes that a measure of the stability of population models in the presence of white noise is given by a Liapunov function for the nonlinear deterministic model, and the implications of the result are examined. We consider next the use of kinetic equations to study physical systems, and prove that the use of higher order derivatives in the Mori formalism leads to results formally identical with Mori's continued fraction theory. We then apply the method of using higher derivatives to develop a physical picture of collective mode dynamics in the linear Heisenberg chain. The collective modes and their time scales are isolated and studied.

Submitted by Maria Cristina (library@lncc.br) on 2015-04-07T14:58:47Z No. of bitstreams: 1 thesis_Simone.pdf: 2489801 bytes, checksum: 45b3a3851811effbf5253248b65db6f0 (MD5) / Approved for entry into archive by Maria Cristina (library@lncc.br) on 2015-04-07T14:59:03Z (GMT) No. of bitstreams: 1 thesis_Simone.pdf: 2489801 bytes, checksum: 45b3a3851811effbf5253248b65db6f0 (MD5) / Made available in DSpace on 2015-04-07T14:59:14Z (GMT). No. of bitstreams: 1 thesis_Simone.pdf: 2489801 bytes, checksum: 45b3a3851811effbf5253248b65db6f0 (MD5) Previous issue date: 2012-03-28 / Biological invasion is a worldwide phenomenon, which can impact on native species, big social and economic losses beyond the reduction of global biodiversity. Recent research indicates that modeling of this problem must integrate natural and social sciences like economy. In this work is proposed a new model for the invasion process, where the invasive species retains temporarily a fraction of the total population in the conquered territory, to establish a self-sustaining population. In this case, the Fick_slaw (classical di_usion), does not represent this problem, since there is a new phenomenon involved in the process which can not be characterized simply by manipulating the diversivity parameters. Thus, it is evaluated that a new model explicitly includes processes for the temporary retention by including a term of fourth order. The problem considered here describes the dynamic population of forward propagating waves that represent the invasion of the exotic species, and is mathematically modeled by transport equations solved numerically using finite element method and the case where the economic efects of invasion were incorporated is solved using control techniques. / Invasão biológica é um fenômeno mundial, que pode causar impactos nas espécies nativas, grandes perdas econômicas e sociais além da diminuição da biodiversidade global. Recentes pesquisas indicam que a modelagem deste tipo de problema deve integrar ciências naturais e sociais como a economia. Neste trabalho, é proposto um novo modelo do processo de invasão, considerando que a espécie invasora mantém temporariamente uma fração da população total no território conquistado, além de estabelecer uma população autossustentável. Neste caso, a distribuição espacial desta espécie não pode ser representada apenas pela lei de Fick (difusão clássica), uma vez que há um fenômeno novo envolvido no processo que não pode ser caracterizado simplesmente manipulando os parâmetros de difusividade. Assim, avalia-se um novo modelo que inclui explicitamente os processos de retenção temporária através da inclusão de um termo de quarta ordem. O problema populacional dinâmico considerado descreve a propagação de frente de ondas que representam a invasão da espécie invasora, e um modelado matematicamente por equações de transporte resolvida numericamente utilizando métodos de elementos finitos e para o caso em que os efeitos econômicos da invasão foram considerados incorpora-se ainda técnicas de controle.

The prediction and analysis of changes in the numbers of biological populations rest on mathematical formulations of demographic events (births and deaths) classified by the age of individuals. The development of demographic theory when birth and death rates vary statistically over time is the central theme of this work. A study of the standard Leslie model for the demographic dynamics of populations in variable environments is made. At each time interval a Leslie matrix of survival rates and fertilities of a population is chosen according to a Markov process and the population numbers in different age classes are computed. Analytical bounds are developed for the logarithmic growth rate and the age-structure of a population after long times. For a two dimensional case, it is shown analytically that a uniform distribution results for the age-structure if the survival rate from the first to the second age-class is a uniformly distributed random quantity with no serial auto correlation. Numerical studies are made which lead to similar conclusions when the survival rate obeys other distributions. It is found that the variance in the survival parameter is linearly related to the variance in the age structure. An efficient algorithm is developed for numerical simulations on a computer by considering a time sequence of births rather than whole populations. The algorithm is then applied to an example in three dimensions to calculate a sequence of births when the survival rate from the first to the second age-class is a random parameter. Numerical values for the logarithmic growth rate and the logarithmic variance for a population and the probability of extinction are obtained and then compared to the analytical results reported here and elsewhere.

This paper presents methods and results of county-level population estimation using Landsat Thematic Mapper (TM) images of Denton County and Collin County in Texas. Landsat TM images acquired in March 2000 were classified into residential and non-residential classes using maximum likelihood classification and knowledge-based classification methods. Accuracy assessment results from the classified image produced using knowledge-based classification and traditional supervised classification (maximum likelihood classification) methods suggest that knowledge-based classification is more effective than traditional supervised classification methods. Furthermore, using randomly selected samples of census block groups, ordinary least squares (OLS) and geographically weighted regression (GWR) models were created for total population estimation. The overall accuracy of the models is over 96% at the county level. The results also suggest that underestimation normally occurs in block groups with high population density, whereas overestimation occurs in block groups with low population density.

Orientadores: Rodney Carlos Bassanezi, Laecio Carvalho de Barros / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-04T03:22:11Z (GMT). No. of bitstreams: 1 Magnago_KarineFaverzani_D.pdf: 4968735 bytes, checksum: d2d7f169f303816c10985c62cb0bb240 (MD5) Previous issue date: 2005 / Resumo: Neste trabalho, nós estudamos o modelo logístico discreto com variável de estado incerta, modelada por meio de subconjuntos fuzzy; determinamos pontos fixos exclusivos da equação fuzzy correspondente, bem como uma família de órbitas periódicas assintoticamente estáveis. Realizamos simulações iterativas que podem também considerar a taxa de crescimento intrínseco incerta. Na seqüência, estudamos modelos de metapopulação de moscas varejeiras, aplicados às espécies Lucilia eximia e Chrysomya albiceps. Utilizamos sistemas baseados em regras fuzzy, com subjetividade de ambiente na estimativa da sobrevivência e migração. Consideramos migração dirigida e habitat fragmentado em sítios com distribuição espacial cíclica ou alinhada. Realizamos a análise dos equilíbrios no caso particular: dois sítios interligados, e simulações nos demais casos. Comparamos o modelo logístico discreto e o modelo local utilizado nos modelos de metapopulação propostos / Abstract: ln this work, we study discrete logistic model with uncertain state variable, modeled by fuzzy subsets; we determine fixed points of corresponding fuzzy equation, as well as a family of stable periodic orbits. We present simulations that can also consider uncertain intrinsic growth rate. We study metapoplllation models of blowfiies applied to the species Lucilia eximia and Chrysomya albiceps. We use fuzzy rules based systems with subjective environment to estimate survival and migration rates. We consider directional migration and habitat broken into fragments at patches with cyclic or aligned space distribution. We analyze the equilibria in the particular case: two interlinked patches, and we simulate in other cases. We compare discrete logistic model and the local model used in the proposed metapopulation models / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

Population estimation in inter-censual years has many important applications. In this research, high-resolution pan-sharpened IKONOS image, LiDAR data, and parcel data are used to estimate small-area population in the eastern part of the city of Denton, Texas. Residential buildings are extracted through object-based classification techniques supported by shape indices and spectral signatures. Three population indicators -building count, building volume and building area at block level are derived using spatial joining and zonal statistics in GIS. Linear regression and geographically weighted regression (GWR) models generated using the three variables and the census data are used to estimate population at the census block level. The maximum total estimation accuracy that can be attained by the models is 94.21%. Accuracy assessments suggest that the GWR models outperformed linear regression models due to their better handling of spatial heterogeneity. Models generated from building volume and area gave better results. The models have lower accuracy in both densely populated census blocks and sparsely populated census blocks, which could be partly attributed to the lower accuracy of the LiDAR data used.