Dynamics in dumbbell domains II. The limiting problem

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The dynamics of a one-dimensional parabolic problem versus the dynamics of its discretization

In this paper we prove that the spatial discretization of a one dimensional system of parabolic equations. with suitably small step size, contains exactly the same asymptotic dynamics as the continuous problem. (C) 2000 Academic Press.

Dynamics in dumbbell domains III. Continuity of attractors

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Patterns in parabolic problems with nonlinear boundary conditions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Reduction of infinite dimensional systems to finite dimensions: Compact convergence approach

We consider parameter dependent semilinear evolution problems for which, at the limit value of the parameter, the problem is finite dimensional. We introduce an abstract functional analytic framework that applies to many problems in the existing literature for which the study of asymptotic dynamics can be reduced to finite dimensions via the invariant manifolds technique. Some practical models are considered to show wide applicability of the theory. © 2013 Society for Industrial and Applied Mathematics.

Perturbation of a nonautonomous problem in ℝn

In this paper, we prove a stability result about the asymptotic dynamics of a perturbed nonautonomous evolution equation in ℝn governed by a maximal monotone operator. Copyright © 2013 John Wiley & Sons, Ltd. Copyright © 2013 John Wiley & Sons, Ltd.

Spatio-temporal dynamics and transition from asymptotic equilibrium to bounded oscillations in Chrysomya albiceps (Diptera, Calliphoridae)

The sensitivity of parameters that govern the stability of population size in Chrysomya albiceps and describe its spatial dynamics was evaluated in this study. The dynamics was modeled using a density-dependent model of population growth. Our simulations show that variation in fecundity and mainly in survival has marked effect on the dynamics and indicates the possibility of transitions from one-point equilibrium to bounded oscillations. C. albiceps exhibits a two-point limit cycle, but the introduction of diffusive dispersal induces an evident qualitative shift from two-point limit cycle to a one fixed-point dynamics. Population dynamics of C. albiceps is here compared to dynamics of Cochliomyia macellaria, C. megacephala and C. putoria.

Dynamics of experimental populations of native and introduced blowflies (Diptera: Calliphoridae): mathematical modelling and the transition from asymptotic equilibrium to bounded oscillations

The equilibrium dynamics of native and introduced blowflies is modelled using a density-dependent model of population growth that takes into account important features of the life-history in these flies. A theoretical analysis indicates that the product of maximum fecundity and survival is the primary determinant of the dynamics. Cochliomyia macellaria, a blowfly native to the Americas and the introduced Chrysomya megacephala and Chrysomya putoria, differ in their dynamics in that the first species shows a damping oscillatory behavior leading to a one-point equilibrium, whereas in the last two species population numbers show a two-point limit cycle. Simulations showed that variation in fecundity has a marked effect on the dynamics and indicates the possibility of transitions from one-point equilibrium to bounded oscillations and aperiodic behavior. Variation in survival has much less influence on the dynamics.

Hartman-Grobman decomposition when in presence of jumps in the relative degree of the dynamics in an energy harvesting device

This work deals with the nonlinear piezoelectric coupling in vibration-based energy harvesting, done by A. Triplett and D.D. Quinn in J. of Intelligent Material Syst. and Structures (2009). In that paper the first order nonlinear fundamental equation has a three dimensional state variable. Introducing both observable and control variables in such a way the controlled system became a SISO system, we can obtain as a corollary that for a particular choice of the observable variable it is possible to present an explicit functional relation between this variable one, and the variable representing the charge harvested. After-by observing that the structure in the Input-Output decomposition essentially changes depending on the relative degree changes, presenting bifurcation branches in its zero dynamics-we are able in to identify this type of bifurcation indicating its close relation with the Hartman - Grobman theorem telling about decomposition into stable and the unstable manifolds for hyperbolic points.

Infrared dynamics in (2+1) dimensions

In this work we study the asymptotic behavior of (2+1)-dimensional quantum electrodynamics in the infrared region. We show that an appropriate redefinition of the fermion current operator leads to an asymptotic evolution operator that contains a divergent Coulomb phase factor and a contribution from the electromagnetic field at large distances, factored from the evolution operator for free fields, and we conclude that the modified scattering operator maps two spaces of coherent states of the electromagnetic field, as in the Kulish-Faddeev model for QED (quantum electrodynamics) in four space-time dimensions.

On the asymptotic behavior of effective QED at finite temperature

The aim of this paper is to study finite temperature effects in effective quantum electrodynamics using Weisskopf's zero-point energy method in the context of thermo, field dynamics. After a general calculation for a weak magnetic field at fixed T, the asymptotic behavior of the Euler-Kockel-Heisenberg Lagrangian density is investigated focusing on the regularization requirements in the high temperature limit. In scalar QED the same problem is also discussed.

Nonlinear dynamics of short traveling capillary-gravity waves

We establish a Green-Nagdhi model equation for capillary-gravity waves in (2+1) dimensions. Through the derivation of an asymptotic equation governing short-wave dynamics, we show that this system possesses (1 + 1) traveling-wave solutions for almost all the values of the Bond number θ (the special case θ=1/3 is not studied). These waves become singular when their amplitude is larger than a threshold value, related to the velocity of the wave. The limit angle at the crest is then calculated. The stability of a wave train is also studied via a Benjamin-Feir modulational analysis. ©2005 The American Physical Society.

Asymptotic approach for the nonlinear equatorial long wave interactions

In the present work we use an asymptotic approach to obtain the long wave equations. The shallow water equation is put as a function of an external parameter that is a measure of both the spatial scales anisotropy and the fast to slow time ratio. The values given to the external parameters are consistent with those computed using typical values of the perturbations in tropical dynamics. Asymptotically, the model converge toward the long wave model. Thus, it is possible to go toward the long wave approximation through intermediate realizable states. With this approach, the resonant nonlinear wave interactions are studied. To simplify, the reduced dynamics of a single resonant triad is used for some selected equatorial trios. It was verified by both theoretical and numerical results that the nonlinear energy exchange period increases smoothly as we move toward the long wave approach. The magnitude of the energy exchanges is also modified, but in this case depends on the particular triad used and also on the initial energy partition among the triad components. Some implications of the results for the tropical dynamics are disccussed. In particular, we discuss the implications of the results for El Nĩo and the Madden-Julian in connection with other scales of time and spatial variability. © Published under licence by IOP Publishing Ltd.