The size of excavators within a polymorphic termite species governs tunnel topology

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

ON THREE-PARAMETER FAMILIES of FILIPPOV SYSTEMS - THE FOLD-SADDLE SINGULARITY

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

NONDEGENERATE UMBILICS, THE PATH FORMULATION and GRADIENT BIFURCATION PROBLEMS

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

Soliton parameters and chaotic sets

In this work we apply a nonperturbative approach to analyze soliton bifurcation ill the presence of surface tension, which is a reformulation of standard methods based on the reversibility properties of the system. The hypothesis is non-restrictive and the results can be extended to a much wider variety of systems. The usual idea of tracking intersections of unstable manifolds with some invariant set is again used, but reversibility plays an important role establishing in a geometrical point of view some kind of symmetry which, in a classical way, is unknown or nonexistent. Using a computer program we determine soliton solutions and also their bifurcations ill the space of parameters giving a picture of the chaotic structural distribution to phase and amplitude shift phenomena. (C) 2009 Published by Elsevier Ltd.

On local analysis of oscillations of a non-ideal and non-linear mechanical model

It is of major importance to consider non-ideal energy sources in engineering problems. They act on an oscillating system and at the same time experience a reciprocal action from the system. Here, a non-ideal system is studied. In this system, the interaction between source energy and motion is accomplished through a special kind of friction. Results about the stability and instability of the equilibrium point of this system are obtained. Moreover, its bifurcation curves are determined. Hopf bifurcations are found in the set of parameters of the oscillating system.

On Nonlinear Dynamics and an Optimal Control Design to a Longitudinal Flight

In this work, we analyzed a bifurcational behavior of a longitudinal flight nonlinear dynamics, taking as an example the F-8 aircraft Crusader. We deal with an analysis of high angles of attack in order to stabilize the oscillations; those were close to the critical angle of the aircraft, in the flight conditions, established. We proposed a linear optimal control design applied to the considered nonlinear aircraft model below angle of stall, taking into account regions of Hopf and saddled noddle bifurcations.

The Feigenbaum's delta for a high dissipative bouncing ball model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Analytical study of the nonlinear behavior of a shape memory oscillator: Part II-resonance secondary

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Statistical properties of a dissipative kicked system: Critical exponents and scaling invariance

A new universal empirical function that depends on a single critical exponent (acceleration exponent) is proposed to describe the scaling behavior in a dissipative kicked rotator. The scaling formalism is used to describe two regimes of dissipation: (i) strong dissipation and (ii) weak dissipation. For case (i) the model exhibits a route to chaos known as period doubling and the Feigenbaum constant along the bifurcations is obtained. When weak dissipation is considered the average action as well as its standard deviation are described using scaling arguments with critical exponents. The universal empirical function describes remarkably well a phase transition from limited to unlimited growth of the average action. (C) 2012 Elsevier B.V. All rights reserved.

Analytical study of the nonlinear behavior of a shape memory oscillator: Part I-primary resonance and free response at low temperatures

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Chaotic vibrations of a nonideal electro-mechanical system

Nonideal systems are those in which one takes account of the influence of the oscillatory system on the energy supply with a limited power (Kononenko, 1969). In this paper, a particular nonideal system is investigated, consisting of a pendulum whose support point is vibrated along a horizontal guide by a two bar linkage driven by a DC motor, considered to be a limited power supply. Under these conditions, the oscillations of the pendulum are analyzed through the variation of a control parameter. The voltage supply of the motor is considered to be a reliable control parameter. Each simulation starts from zero speed and reaches a steady-state condition when the motor oscillates around a medium speed. Near the fundamental resonance region, the system presents some interesting nonlinear phenomena, including multi-periodic, quasiperiodic, and chaotic motion. The loss of stability of the system occurs through a saddle-node bifurcation, where there is a collision of a stable orbit with an unstable one, which is approximately located close to the value of the pendulum's angular displacement given by alpha (C)= pi /2. The aims of this study are to better understand nonideal systems using numerical simulation, to identify the bifurcations that occur in the system, and to report the existence of a chaotic attractor near the fundamental resonance. (C) 2001 Elsevier B.V. Ltd. All rights reserved.

Reversible equivariant Hopf bifurcation

In this paper we study codimension-one Hopf bifurcation from symmetric equilibrium points in reversible equivariant vector fields. Such bifurcations are characterized by a doubly degenerate pair of purely imaginary eigenvalues of the linearization of the vector field at the equilibrium point. The eigenvalue movements near such a degeneracy typically follow one of three scenarios: splitting (from two pairs of imaginary eigenvalues to a quadruplet on the complex plane), passing (on the imaginary axis), or crossing (a quadruplet crossing the imaginary axis). We give a complete description of the behaviour of reversible periodic orbits in the vicinity of such a bifurcation point. For non-reversible periodic solutions. in the case of Hopf bifurcation with crossing eigenvalues. we obtain a generalization of the equivariant Hopf Theorem.

The defocusing mechanism of isochronous resonances

We present a numerical study concerning the defocusing mechanism of isochronous resonance island chains in the presence of two permanent robust tori. The process is initialized and concluded through bifurcations of fixed points located on the robust tori. Our approach is based on a Hamiltonian system derived from the resonant normal form. Choosing a convenient parameter in this system, we are able to depict a comprehensive analysis of the dynamics of the problem. (c) 2004 Elsevier B.V. All rights reserved.

Carbon monoxide oxidation over platinum: Stable, oscillatory and quasi-chaotic regimes

We model the heterogeneously catalyzed oxidation of CO over a Pt surface. A phase diagram analysis is used to probe the several steady state regimes and their stability. We incorporate an experimentally observed 'slow' sub-oxide kinetic step, thereby generalizing a previously presented model. In agreement with experimental data, stable, oscillatory and quasi-chaotic regimes are obtained. Furthermore, the inclusion of the sub-oxide step yields a relaxation oscillation regime. © 1998 Elsevier Science B.V. All rights reserved.

Atherosclerosis morphology and pathogenesis

Atherosclerosis is a very common and important disease being the most important cause of mortality in Brazil. Indeed, in 1995, 23.3% of deaths, all ages, in our country, were the consequence of atherosclerosis. This percentage grows to 26.3% for S. Paulo and 32.7% for Rio Grande do Sul. Morphologically, there are 3 main types of lesions: fatty streaks, fibrous plaques, and complicated lesions. Fatty streaks are inocuous and occur early in life. In some persons, with age, they change into fibrous plaques that may lead to stenosis. They also may become complicated by erosion, calcification, hemorrhage and thrombosis. Atherosclerosis is initiated by endothelial functional alterations responsible for increase in permeability to macromolecules, adhesion, and migration of monocytes-macrophages and lymphocytes plus recruitment of platelets and smooth-muscle medial cells. Adhesion molecules, cytokines, growth factors, and free radicals are locally synthesized, favoring proliferation of extracellular matrix and progression of the lesion. Experimental, clinical, and epidemiological evidence point to the importance of lipids, mainly cholesterol-rich low-density lipoprotein (LDL), as one of the most important molecules involved in the genesis and progression of atherosclerosis. Patients with a genetic disorder of cholesterol metabolism (familial hyperlipidemia), caused by a decrease in the availability of receptors for LDL, develop severe atherosclerosis early in life. A series of other factors, such as age, diabetes melitus, diet, hypertension, lack of exercise, elevated hemocysteinemia, immunological disorders, and coagulation instability, are related to the progression of atherosclerosis. All of them are capable of altering the endothelium or increasing the offer of LDL. All the above-mentioned factors are systemic; but atherosclerosic lesions are focal, located at preferential sites such as the emergence of colaterals, bifurcations, and curvatures of arteries, all areas in which the laminar flow is disturbed. In these areas shear stress is diminished favoring the prolongation of permanence time of lipid particles, cells, cytokines, growth factors, etc., in the vicinity of the endothelium. Moreover, the endothelium has sensors that act as transducers of mechanical forces in biological responses. Experimental data demonstrate that the number and quality of adhesion molecules, cytokines, and growth factors synthetized, as well as the local production of radicals, and pro and anticoagulation factors may change with shear stress favoring or not the local establishment and progression of atherosclerotic lesions.