Estabilidade global e bifurcação de Hopf em um modelo de HIV baseado em sistemas do tipo Lotka-Volterra

Pós-graduação em Matematica Aplicada e Computacional - FCT

Transformadas integrais, modelagem fracionária e o sistema de Lotka-Volterra

Pós-graduação em Biometria - IBB

Modelo de Lotka-Volterra com inclusão de termos perturbativos e capacitivos

Our purpose is to show the effects in the predator-prey trajectories due to parameter temporal perturbations and/or inclusion of capacitive terms in the Lotka Volterra Model. An introduction to the Lotka Volterra Model (chapter 2) required a brief review of nonlinear differential equations and stability analysis (chapter 1) , for a better understanding of our work. In the following chapters we display in sequence our results and discussion for the randomic pertubation case (chapter 3); periodic perturbation (chapter 4) and inclusion of capacitive terms (chapter 5). Finally (chapter 6) we synthesize our result

A Periodic Lotka-Volterra System

In this paper periodic time-dependent Lotka-Volterra systems are considered. It is shown that such a system has positive periodic solutions. It is done without constructive conditions over the period and the parameters.

Competitive processes in controlled cationic ring-opening polymerization of oxetane:a Lotka-Volterra predator-prey model of two growing species competing for the same resources

The activation-deactivation pseudo-equilibrium coefficient Qt and constant K0 (=Qt x PaT1,t = ([A1]x[Ox])/([T1]x[T])) as well as the factor of activation (PaT1,t) and rate constants of elementary steps reactions that govern the increase of Mn with conversion in controlled cationic ring-opening polymerization of oxetane (Ox) in 1,4-dioxane (1,4-D) and in tetrahydropyran (THP) (i.e. cyclic ethers which have no homopolymerizability (T)) were determined using terminal-model kinetics. We show analytically that the dynamic behavior of the two growing species (A1 and T1) competing for the same resources (Ox and T) follows a Lotka-Volterra model of predator-prey interactions. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Cost-effective suppression and eradication of invasive predators

Introduced predators can have pronounced effects on naïve prey species; thus, predator control is often essential for conservation of threatened native species. Complete eradication of the predator, although desirable, may be elusive in budget-limited situations, whereas predator suppression is more feasible and may still achieve conservation goals. We used a stochastic predator-prey model based on a Lotka-Volterra system to investigate the cost-effectiveness of predator control to achieve prey conservation. We compared five control strategies: immediate eradication, removal of a constant number of predators (fixed-number control), removal of a constant proportion of predators (fixed-rate control), removal of predators that exceed a predetermined threshold (upper-trigger harvest), and removal of predators whenever their population falls below a lower predetermined threshold (lower-trigger harvest). We looked at the performance of these strategies when managers could always remove the full number of predators targeted by each strategy, subject to budget availability. Under this assumption immediate eradication reduced the threat to the prey population the most. We then examined the effect of reduced management success in meeting removal targets, assuming removal is more difficult at low predator densities. In this case there was a pronounced reduction in performance of the immediate eradication, fixed-number, and lower-trigger strategies. Although immediate eradication still yielded the highest expected minimum prey population size, upper-trigger harvest yielded the lowest probability of prey extinction and the greatest return on investment (as measured by improvement in expected minimum population size per amount spent). Upper-trigger harvest was relatively successful because it operated when predator density was highest, which is when predator removal targets can be more easily met and the effect of predators on the prey is most damaging. This suggests that controlling predators only when they are most abundant is the "best" strategy when financial resources are limited and eradication is unlikely. © 2008 Society for Conservation Biology.

Singularity structure of third-order dynamical systems .2

The singularity structure of the solutions of a general third-order system, with polynomial right-hand sides of degree less than or equal to two, is studied about a movable singular point, An algorithm for transforming the given third-order system to a third-order Briot-Bouquet system is presented, The dominant behavior of a solution of the given system near a movable singularity is used to construct a transformation that changes the given system directly to a third-order Briot-Bouquet system. The results of Horn for the third-order Briot-Bouquet system are exploited to give the complete form of the series solutions of the given third-order system; convergence of these series in a deleted neighborhood of the singularity is ensured, This algorithm is used to study the singularity structure of the solutions of the Lorenz system, the Rikitake system, the three-wave interaction problem, the Rabinovich system, the Lotka-Volterra system, and the May-Leonard system for different sets of parameter values. The proposed approach goes far beyond the ARS algorithm.

Prediction, Chaos and Ecological Perspective.

As defined, the modeling procedure is quite broad. For example, the chosen compartments may contain a single organism, a population of organisms, or an ensemble of populations. A population compartment, in turn, could be homogeneous or possess structure in size or age. Likewise, the mathematical statements may be deterministic or probabilistic in nature, linear or nonlinear, autonomous or able to possess memory. Examples of all types appear in the literature. In practice, however, ecosystem modelers have focused upon particular types of model constructions. Most analyses seem to treat compartments which are nonsegregated (populations or trophic levels) and homogeneous. The accompanying mathematics is, for the most part, deterministic and autonomous. Despite the enormous effort which has gone into such ecosystem modeling, there remains a paucity of models which meets the rigorous &! validation criteria which might be applied to a model of a mechanical system. Most ecosystem models are short on prediction ability. Even some classical examples, such as the Lotka-Volterra predator-prey scheme, have not spawned validated examples.

Uma abordagem por meio da teoria dos jogos de um modelo em ecologia matemática

A presente dissertação propõe uma abordagem alternativa na simulação matemática de um cenário preocupante em ecologia: o controle de pragas nocivas a uma dada lavoura de soja em uma específica região geográfica. O instrumental teórico empregado é a teoria dos jogos, de forma a acoplar ferramentas da matemática discreta à análise e solução de problemas de valor inicial em equações diferenciais, mais especificamente, as chamadas equações de dinâmica populacional de Lotka-Volterra com competição. Essas equações, que modelam o comportamento predador-presa, possuem, com os parâmetros inicialmente utilizados, um ponto de equilíbrio mais alto que o desejado no contexto agrícola sob exame, resultando na necessidade de utilização da teoria do controle ótimo. O esquema desenvolvido neste trabalho conduz a ferramentas suficientemente simples, de forma a tornar viável o seu uso em situações reais. Os dados utilizados para o tratamento do problema que conduziu a esta pesquisa interdisciplinar foram coletados de material bibliográfico da Empresa Brasileira de Pesquisa Agropecuária EMBRAPA.

蓖齿眼子菜对栅藻和微囊藻的他感作用及其参数

主要报道篦齿眼子菜 (俗称红线草 )的种植水抽滤液对栅藻、微囊藻生长的他感作用试验。应用修正的逻辑斯谛 (Logistic)方程和Lotka Volterra种群竞争模型来计算篦齿眼子菜对藻类的他感作用参数。纯培养试验结果表明 :种植水抽滤液对栅藻生物量和生长率都有一定的促进作用。当浓度大于等于 5 0 %时 ,对栅藻生长的影响则是有抑制效应 ,他感作用效应与种植水的浓度没有明显的相关性 ,他感作用参数平均为 - 0 0 2 6。所有浓度设对照。微囊藻的生长都有明显的抑制作用 ,他感作用参数平均为 - 0

以营养动力学为基础的种间竞争模型的建立

本文从生物种群增长的营养动力学理论出发，建立了一个新的种间竞争的数学模型，这是单种群增长的崔-Iawson模型在种间竞争中的发展和推广。二者有着共同的比较真实可靠的理论基础。新的种间竞争模型在特殊条件下转化为经典的Lotka-Volterra竞争方程，二者有着相同的定性行为，但是，用作者提出的种群竞争力指数，新的种间竞争模型能够能够给予种间竞争结局一个符合生物、生态学原理的解，而且，新的种间竞争模型在定量行为上大大扩充了Lotka-Volterra竞争方程，例如，以非线性种内，种间竞争功能反应代替了Lotka-Volterra竞争方程线性种内、种间竞争功能反应。因此，新的种间竞争模型是对经典的Lotka-Volterra竞争方程的扩充。对Gause的原生Paramecium和caudatum Stylonychia mytilus种竞争实验的数据拟合表明，新的种间竞争模型与种间竞争实验结果达到非常好的吻合，相反，Lotka-Volterra竞争方程拟合效果很差。将新的种间竞争模型尝试性地应用于长白山北坡岳桦云冷杉林的优势树种的动态特性分析和预测，也得到良好的结果。本项研究弥补了生物种群增长的营养动力学研究在种间竞争方面的不足；克服了经典的Lotka-Volterra竞争方程及其他种间竞争模型的局限，发展和完善了种间竞争的理论；这对于促进生态学向成熟发展具有重要意义。

长白山北坡森林群落交错区优势树种动态(英文)

基于28个20mx90m样地的调查数据,利用Lotka-Volterra模型,本文分析了长白山北坡阔叶红松(Pinuskoraiensis)林和云冷杉林(也叫暗针叶林)群落交错区优势树种之间的竞争及动态。结果显示:在自然条件下,群落将向两个方向分化,一是以云杉(PiceajezoensisandP.koraiensis)和冷杉(Abiesnephrolepis)为优势的群落,并在达到平衡时冷杉占绝对优势(相对优势度的77.1%):另一种是以红松或云冷杉和阔叶树占绝对优势的针阔混交林,并在达到平衡时,阔叶树在阔叶红松林中占相对优势度的50%,在云冷杉一阔叶林类型中占66%。同时,本研究说明:(1)阔叶红松林和云冷杉林都是长白山气候顶极群落:(2)交错区具有过渡性质:(3)森林群落的分化结果说明演替的方向受局部生境的影响。图1表3参24。