Control aspects in nonlinear Hill's equation

The Hill's equations-even in the linear original version are a describer of phenomenon having chaotic flavor, giving sometimes very unusual situations. The theory of the so called intervals of instability in the equation provides the precise description for most of these phenomena. Considerations on nonlinearities into the Hill's equation is a quite recent task. The linearized version for almost of these systems it reduces to the Hill's classical linear one. In this paper, some indicative facts are pointed out on the possibility of having the linear system stabilizable and/or exactly controllable. As consequence of such an approach we get results having strong classical aspects, like the one talking about location of parameters in intervals of stability. A result for nonlinear proper periodic controls, is considered too. (C) 2010 Elsevier B.V. All rights reserved.

Regularization and singular perturbation techniques for non-smooth systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice

Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with one-dimensional (1D) conservative plus dissipative nonlinear optical lattices, are investigated. In the case of focusing media (with attractive atomic systems), the collapse of the wave packet is arrested by the dissipative periodic nonlinearity. The adiabatic variation of the background scattering length leads to metastable matter-wave solitons. When the atom feeding mechanism is used, a dissipative soliton can exist in focusing 2D media with 1D periodic nonlinearity. In the defocusing media (repulsive BEC case) with harmonic trap in one direction and nonlinear optical lattice in the other direction, the stable soliton can exist. Variational approach simulations are confirmed by full numerical results for the 2D Gross-Pitaevskii equation.

Stability analysis of the D-dimensional nonlinear Schrodinger equation with trap and two- and three-body interactions

Considering the static solutions of the D-dimensional nonlinear Schrodinger equation with trap and attractive two-body interactions, the existence of stable solutions is limited to a maximum critical number of particles, when D greater than or equal to 2. In case D = 2, we compare the variational approach with the exact numerical calculations. We show that, the addition of a positive three-body interaction allows stable solutions beyond the critical number. In this case, we also introduce a dynamical analysis of the conditions for the collapse. (C) 2000 Published by Elsevier B.V. B.V. All rights reserved.

Universality of Brunnian (N-body Borromean) four- and five-body systems

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

Soliton dynamics at an interface between a uniform medium and a nonlinear optical lattice

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

Nonlinear two-field models from orbit equation deformations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Nonlinear Interactions in a Piezoceramic Bar Transducer Powered by a Vacuum Tube Generated by a Nonideal Source

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Mathematical modeling and control of population systems: Applications in biological pest control

The aim of this paper is to apply methods from optimal control theory, and from the theory of dynamic systems to the mathematical modeling of biological pest control. The linear feedback control problem for nonlinear systems has been formulated in order to obtain the optimal pest control strategy only through the introduction of natural enemies. Asymptotic stability of the closed-loop nonlinear Kolmogorov system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation, thus guaranteeing both stability and optimality. Numerical simulations for three possible scenarios of biological pest control based on the Lotka-Volterra models are provided to show the effectiveness of this method. (c) 2007 Elsevier B.V. All rights reserved.

Suppression of vibrations in strongly nonhomogeneous 2DOF systems

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

On control and synchronization in chaotic and hyperchaotic systems via linear feedback control

This paper presents the control and synchronization of chaos by designing linear feedback controllers. The linear feedback control problem for nonlinear systems has been formulated under optimal control theory viewpoint. Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation thus guaranteeing both stability and optimality. The formulated theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations were provided in order to show the effectiveness of this method for the control of the chaotic Rossler system and synchronization of the hyperchaotic Rossler system. (C) 2007 Elsevier B.V. All rights reserved.

Introduction to Focus Issue: Statistical mechanics and billiard-type dynamical systems

Dynamical systems of the billiard type are of fundamental importance for the description of numerous phenomena observed in many different fields of research, including statistical mechanics, Hamiltonian dynamics, nonlinear physics, and many others. This Focus Issue presents the recent progress in this area with contributions from the mathematical as well as physical stand point. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4730155]

VERY RAPIDLY VARYING BOUNDARIES IN EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS. THE CASE of A NON UNIFORMLY LIPSCHITZ DEFORMATION

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

Study of stayability in Nellore cows using a threshold model

The objectives of the current study were to assess the feasibility of using stayability traits to improve fertility of Nellore cows and to examine the genetic relationship among the stayabilities at different ages. Stayability was defined as whether a cow calved every year up to the age of 5 (Stay5), 6 (Stay6), or 7 (Stay7) yr of age or more, given that she was provided the opportunity to breed. Data were analyzed based on a maximum a posteriori probit threshold model to predict breeding values on the liability scale, whereas the Gibbs sampler was used to estimate variance components. The EBV were obtained using all animals included in the pedigree or bulls with at least 10 daughters with stayability observations, and average genetic trends were obtained in the liability and transformed to the probability scale. Additional analyses were performed to study the genetic relationship among stayability traits, which were compared by contrasting results in terms of EBV and the average genetic superiority as a function of the selected proportion of sires. Heritability estimates and SD were 0.25 +/- 0.02, 0.22 +/- 0.03, and 0.28 +/- 0.03 for Stay5, Stay6, and Stay7, respectively. Average genetic trends, by year, were 0.51 +/- 0.34, and 0.38% for Stay5, Stay6, and Stay7, respectively. Estimates of EBV SD, in the probability scale, for all animals included in the pedigree and for bulls with at least 10 daughters with stayability observations were 7.98 and 12.95, 6.93 and 11.38, and 8.24 and 14.30% for Stay5, Stay6, and Stay7, respectively. A reduction in the average genetic superiorities in Stay7 would be expected if the selection were based on Stay5 or Stay6. Nonetheless, the reduction in EPD, depending on selection intensity, is on average 0.74 and 1.55%, respectively. Regressions of the sires' EBV for Stay5 and Stay6 on the sires' EBV for Stay7 confirmed these results. The heritability and genetic trend estimates for all stayability traits indicate that it is possible to improve fertility with selection based on a threshold analysis of stayability. The SD of EBV for stayability traits show that there is adequate genetic variability among animals to justify inclusion of stayability as a selection criterion. The potential linear relationship among stayability traits indicates that selection for improved female traits would be more effective by having predictions on the Stay5 trait.