Suppressing grazing chaos in impacting system by structural nonlinearity

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing. (C) 2007 Elsevier Ltd. All rights reserved.

Chaotic transport in reversed shear tokamaks

For tokamak models using simplified geometries and reversed shear plasma profiles, we have numerically investigated how the onset of Lagrangian chaos at the plasma edge may affect the plasma confinement in two distinct but closely related problems. Firstly, we have considered the motion of particles in drift waves in the presence of an equilibrium radial electric field with shear. We have shown that the radial particle transport caused by this motion is selective in phase space, being determined by the resonant drift waves and depending on the parameters of both the resonant waves and the electric field profile. Moreover, we have shown that an additional transport barrier may be created at the plasma edge by increasing the electric field. In the second place, we have studied escape patterns and magnetic footprints of chaotic magnetic field lines in the region near a tokamak wall, when there are resonant modes due to the action of an ergodic magnetic limiter. A non-monotonic safety factor profile has been used in the analysis of field line topology in a region of negative magnetic shear. We have observed that, if internal modes are perturbed, the distributions of field line connection lengths and magnetic footprints exhibit spatially localized escape channels. For typical physical parameters of a fusion plasma, the two Lagrangian chaotic processes considered in this work can be effective in usual conditions so as to influence plasma confinement. The reversed shear effects discussed in this work may also contribute to evaluate the transport barrier relevance in advanced confinement scenarios in future tokamak experiments.

CRITICAL BEHAVIOR AND THRESHOLD OF COEXISTENCE OF A PREDATOR-PREY STOCHASTIC MODEL IN A 2D LATTICE

We investigate the critical behavior of a stochastic lattice model describing a predator-prey system. By means of Monte Carlo procedure we simulate the model defined on a regular square lattice and determine the threshold of species coexistence, that is, the critical phase boundaries related to the transition between an active state, where both species coexist and an absorbing state where one of the species is extinct. A finite size scaling analysis is employed to determine the order parameter, order parameter fluctuations, correlation length and the critical exponents. Our numerical results for the critical exponents agree with those of the directed percolation universality class. We also check the validity of the hyperscaling relation and present the data collapse curves.

Experimental characterization of nonlinear systems: a real-time evaluation of the analogous Chua`s circuit behavior

This paper presents an experimental characterization of the behavior of an analogous version of the Chua`s circuit. The electronic circuit signals are captured using a data acquisition board (DAQ) and processed using LabVIEW environment. The following aspects of the time series analysis are analyzed: time waveforms, phase portraits, frequency spectra, Poincar, sections, and bifurcation diagram. The circuit behavior is experimentally mapped with the parameter variations, where are identified equilibrium points, periodic and chaotic attractors, and bifurcations. These analysis techniques are performed in real-time and can be applied to characterize, with precision, several nonlinear systems.

MODELING THE EVOLUTION OF COMPLEX NETWORKS THROUGH THE PATH-STAR TRANSFORMATION AND OPTIMAL MULTIVARIATE METHODS

The topology of real-world complex networks, such as in transportation and communication, is always changing with time. Such changes can arise not only as a natural consequence of their growth, but also due to major modi. cations in their intrinsic organization. For instance, the network of transportation routes between cities and towns ( hence locations) of a given country undergo a major change with the progressive implementation of commercial air transportation. While the locations could be originally interconnected through highways ( paths, giving rise to geographical networks), transportation between those sites progressively shifted or was complemented by air transportation, with scale free characteristics. In the present work we introduce the path-star transformation ( in its uniform and preferential versions) as a means to model such network transformations where paths give rise to stars of connectivity. It is also shown, through optimal multivariate statistical methods (i.e. canonical projections and maximum likelihood classification) that while the US highways network adheres closely to a geographical network model, its path-star transformation yields a network whose topological properties closely resembles those of the respective airport transportation network.

ENHANCING MULTISCALE FRACTAL DESCRIPTORS USING FUNCTIONAL DATA ANALYSIS

This work presents a novel approach in order to increase the recognition power of Multiscale Fractal Dimension (MFD) techniques, when applied to image classification. The proposal uses Functional Data Analysis (FDA) with the aim of enhancing the MFD technique precision achieving a more representative descriptors vector, capable of recognizing and characterizing more precisely objects in an image. FDA is applied to signatures extracted by using the Bouligand-Minkowsky MFD technique in the generation of a descriptors vector from them. For the evaluation of the obtained improvement, an experiment using two datasets of objects was carried out. A dataset was used of characters shapes (26 characters of the Latin alphabet) carrying different levels of controlled noise and a dataset of fish images contours. A comparison with the use of the well-known methods of Fourier and wavelets descriptors was performed with the aim of verifying the performance of FDA method. The descriptor vectors were submitted to Linear Discriminant Analysis (LDA) classification method and we compared the correctness rate in the classification process among the descriptors methods. The results demonstrate that FDA overcomes the literature methods (Fourier and wavelets) in the processing of information extracted from the MFD signature. In this way, the proposed method can be considered as an interesting choice for pattern recognition and image classification using fractal analysis.

THE EFFECT OF CORTICO-THALAMIC CONNECTIONS ON THE DIVERSITY OF CORTICAL ACTIVATIONS AS MODELED BY THE ISING MODEL

The influence of the thalamus on the diversity of cortical activations is investigated in terms of the Ising model with respect to progressive levels of cortico-thalamic connectivity. The results show that better diversity is achieved at lower modulation levels, being higher than those obtained with counterpart network models.

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.

Hopf Bifurcations in a Watt Governor with a Spring

This paper pursues the study carried out in [ 10], focusing on the codimension one Hopf bifurcations in the hexagonal Watt governor system. Here are studied Hopf bifurcations of codimensions two, three and four and the pertinent Lyapunov stability coefficients and bifurcation diagrams. This allows to determine the number, types and positions of bifurcating small amplitude periodic orbits. As a consequence it is found an open region in the parameter space where two attracting periodic orbits coexist with an attracting equilibrium point.

On the motion under focal attraction in a rotating medium

New results are established here on the phase portraits and bifurcations of the kinematic model in system (1), first presented by H.K. Wilson in [3], and by him attributed to L. Markus (unpublished). A new, self-sufficient, study which extends that of [3] and allows an essential conclusion for the applicability of the model is reported here.

Multiple Brake Orbits and Homoclinics in Riemannian Manifolds

Let (M, g) be a complete Riemannian manifold, Omega subset of Man open subset whose closure is homeomorphic to an annulus. We prove that if a,Omega is smooth and it satisfies a strong concavity assumption, then there are at least two distinct geodesics in starting orthogonally to one connected component of a,Omega and arriving orthogonally onto the other one. Using the results given in Giamb et al. (Adv Differ Equ 10:931-960, 2005), we then obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a class of Hamiltonian systems. Under a further symmetry assumption, the result is improved by showing the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinic orbits. In our proof we shall use recent deformation results proved in Giamb et al. (Nonlinear Anal Ser A: Theory Methods Appl 73:290-337, 2010).

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.