Cascades of Hopf bifurcations from boundary delay

We consider a 1-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We deal with non-negative solutions and analyze the stability behavior of its unique positive equilibrium solution, which is given by the constant function u equivalent to 1. We show that if the delay is small, this equilibrium solution is asymptotically stable, similar as in the case without delay. We also show that, as the delay goes to infinity, this equilibrium becomes unstable and undergoes a cascade of Hopf bifurcations. The structure of this cascade will depend on the parameters appearing in the equation. This equation shows some dynamical behavior that differs from the case where the nonlinearity with delay is in the interior of the domain. (C) 2009 Elsevier Inc. All rights reserved.

ON THE SUPERCRITICALITY OF THE FIRST HOPF BIFURCATION IN A DELAY BOUNDARY PROBLEM

The goal of this paper is to analyze the character of the first Hopf bifurcation (subcritical versus supercritical) that appears in a one-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We showed in the previous work [Arrieta et al., 2010] that if the delay is small, the unique non-negative equilibrium solution is asymptotically stable. We also showed that, as the delay increases and crosses certain critical value, this equilibrium becomes unstable and undergoes a Hopf bifurcation. This bifurcation is the first one of a cascade occurring as the delay goes to infinity. The structure of this cascade will depend on the parameters appearing in the equation. In this paper, we show that the first bifurcation that occurs is supercritical, that is, when the parameter is bigger than the delay bifurcation value, stable periodic orbits branch off from the constant equilibrium.

Using ant colonies for solve the multiprocessor task graph scheduling

The problem of scheduling a parallel program presented by a weighted directed acyclic graph (DAG) to the set of homogeneous processors for minimizing the completion time of the program has been extensively studied as academic optimization problem which occurs in optimizing the execution time of parallel algorithm with parallel computer.In this paper, we propose an application of the Ant Colony Optimization (ACO) to a multiprocessor scheduling problem (MPSP). In the MPSP, no preemption is allowed and each operation demands a setup time on the machines. The problem seeks to compose a schedule that minimizes the total completion time.We therefore rely on heuristics to find solutions since solution methods are not feasible for most problems as such. This novel heuristic searching approach to the multiprocessor based on the ACO algorithm a collection of agents cooperate to effectively explore the search space.A computational experiment is conducted on a suit of benchmark application. By comparing our algorithm result obtained to that of previous heuristic algorithm, it is evince that the ACO algorithm exhibits competitive performance with small error ratio.

Programação estocástica para fundos de pensão

Nesta dissertação discutiremos modelos e métodos de soluções de programação estocástica para resolver problemas de ALM em fundos de pensão. Apresentaremos o modelo de (Drijver et al.), baseado na programação estocástica multiestágios inteira-mista. Um estudo de caso para um problema de ALM será apresentado usando simulação de cenários.

Boron adsorption in lowland soils from Parana State, Brazil

Boron adsorption by soil is the main phenomenon that affects its availability to plants. This, the present study investigated the effect of liming on B adsorption by lowland soils of Parana State, and to correlate these values with the physical and chemical properties of the soils. Surface samples of three lowland soils [Gleissolo Haplico (GX), Plintossolo Haplico (FX) and Cambissolo Haplico (CX)], with different origin material and physicochemical properties were used. Samples with or without liming application were incubated during 60 days. Boron adsorption was accomplished by shaking 4.0g soil samples, for 24 h, with 20 mL of 0.01 mol L-1 CaCl2 solution containing different concentrations of B (0, 1, 2, 4, 8 and 16 mg L-1). Sorption was fitted to non-linear form of the Langmuir adsorption isotherm. The adsorption isotherms indicated that the B adsorption increased with its increasing concentration in the equilibrium solution. Maximum adsorption capacity of B ranged from 3.0 to 13.9 mg kg(-1) (without liming) and 14.7 to 35.7 mg kg(-1) (with liming). Liming increased the amount of adsorbed B in Gleissolo Haplico and Plintossolo Haplico soils, although the bonding energy has decreased. The amount of adsorbed B by Cambissolo Haplico soil was not affected by liming application. The most important soil properties affecting the B adsorption in lowland soils were pH, clay content, exchangeable aluminum and iron oxide contents.

Inferência fuzzy para o problema de corte de estoque com sobras aproveitáveis de material

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Solução do problema de corte bidimensional de peças retângulares tipo não-guilhotinado usando simulated annealing

Pós-graduação em Engenharia Elétrica - FEIS

Estudo dos métodos de solução da equação de Fokker-Planck linear e não linear

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Contribuições para o problema de corte de estoque bidimensional na indústria moveleira

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Modelagem matemática e aplicações do problema de coloração em grafos

Pós-graduação em Matemática - IBILCE

Adsorção e disponibilidade de fósforo para o crescimento inicial de mamoneira em solos com diferentes classes texturais

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Mathematical modeling and analysis of the flocculation process in chambers in series

In this study, the flocculation process in continuous systems with chambers in series was analyzed using the classical kinetic model of aggregation and break-up proposed by Argaman and Kaufman, which incorporates two main parameters: K (a) and K (b). Typical values for these parameters were used, i. e., K (a) = 3.68 x 10(-5)-1.83 x 10(-4) and K (b) = 1.83 x 10(-7)-2.30 x 10(-7) s(-1). The analysis consisted of performing simulations of system behavior under different operating conditions, including variations in the number of chambers used and the utilization of fixed or scaled velocity gradients in the units. The response variable analyzed in all simulations was the total retention time necessary to achieve a given flocculation efficiency, which was determined by means of conventional solution methods of nonlinear algebraic equations, corresponding to the material balances on the system. Values for the number of chambers ranging from 1 to 5, velocity gradients of 20-60 s(-1) and flocculation efficiencies of 50-90 % were adopted.

A genetic algorithm/mathematical programming approach to solve a two-level soft drink production problem

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Modelos Matemáticos e Métodos de Solução para Problemas de Dimensionamento de Lotes

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

NASH game and mixed H2/H∞ control

In this work a Nonzero-Sum NASH game related to the H2 and H∞ control problems is formulated in the context of convex optimization theory. The variables of the game are limiting bounds for the H2 and H∞ norms, and the final controller is obtained as an equilibrium solution, which minimizes the `sensitivity of each norm' with respect to the other. The state feedback problem is considered and illustrated by numerical examples.