Synchronization of coupled limit cycles

A unified approach for analyzing synchronization in coupled systems of autonomous differential equations is presented in this work. Through a careful analysis of the variational equation of the coupled system we establish a sufficient condition for synchronization in terms of the geometric properties of the local limit cycles and the coupling operator. This result applies to a large class of differential equation models in physics and biology. The stability analysis is complemented with a discussion of numerical simulations of a compartmental model of a neuron.Comment: Journal of Nonlinear Science, accepte

An accelerated triangulation method for computing the skeletons of free-form solid models

Shape skeletons are powerful geometric abstractions that provide useful intermediate representations for a number of geometric operations on solid models includingfeature recognition, shape decomposition, finite element mesh generation, and shape design. As a result there has been significant interest in the development of effectivemethods for skeleton generation of general free-form solids. In this paper we describe a method that combines Delaunay triangulation with local numerical optimizationschemes for the generation of accurate skeletons of 3D implicit solid models. The proposed method accelerates the slow convergence of Voronoi diagrams to theskeleton, which, without optimization, would require impractically large sample point sets and resulting messhes to attain acceptable accuracy. The Delaunaytriangulation forms the basis for generating the topological structure of the skeleton. The optimization step of the process generates the geometry of the skeleton patchesby moving the vertices of Delaunay tetrahedra and relocating their centres to form maximally inscribed spheres. The computational advantage of the optimization schemeis that it involves the solution of one small optimization problem per tetrahedron and its complexity is therefore only linear (O(n)) in the number of points used for theskeleton approximation. We demonstrate the effectiveness of the method on a number of representative solid models

Biologia floral e sistema de polinização de Solanum stramonifolium Jacq. (Solanaceae) em remanescente de Mata Atlântica, Pernambuco Floral biology and pollination system of Solanum stramonifolium Jacq. (Solanaceae) in an Atlantic Forest remnant in Pernambuco

A deiscência de anteras através de pequenos poros apicais é uma característica encontrada em várias espécies da família Solanaceae, especialmente no gênero Solanum, característica esta que restringe a polinização a um grupo de abelhas fêmeas capazes de vibrar as anteras para retirada do pólen. A fenologia, biologia floral e a polinização de Solanum stramonifolium foram estudadas entre os meses de agosto/1999 a dezembro/2000 em populações naturais ocorrentes no Parque Estadual de Dois Irmãos, um dos poucos remanescentes de Mata Atlântica localizada em Recife, Pernambuco (8°7'30"S e 34°52'30"W). Solanum stramonifolium é um arbusto com flores dispostas em inflorescências racemosas, apresentando corola branca e cinco estames de um amarelo intenso, com anteras poricidas dispostas ao redor do gineceu. A antese ocorre nas primeiras horas do dia, havendo reflexão de luz ultravioleta e presença de áreas de concentração de emissão de odor por toda a corola e na região apical das anteras. Solanum stramonifolium tem padrão de floração contínuo e apresenta flores hermafroditas (62%) e funcionalmente masculinas (38%), o que caracteriza a espécie como andromonóica.Treze espécies de abelhas foram observadas visitando as flores de S. stramonifolium (nove polinizadores e quatro pilhadores). A constante e grande produção de flores faz com que Solamun stramonifolium mantenha sua guilda de polinizadores e garanta assim a sua reprodução, sendo, ao mesmo tempo, uma importante fonte de recursos para a manutenção destas abelhas.<br>The anthers deiscense through two small apical pores is a feature found in many species of Solanaceae, especially in the genus Solanum. This feature restricts pollination to a group of female bees which are able to vibrate the anthers (buzz pollination). The phenology, floral biology and pollination of Solanum stramonifolium were studied between August/1999 and December/2000 in natural populations occurring at Dois Irmãos State Park, one of the last Atlantic forest remnants in Recife city, Pernambuco state (8°7'30"S and 34°52'30"W). Solanum stramonifolium is a shrub whose flowers are arranged in a racemose inflorescence and have white corolla and five stamens with poricide anthers disposed around the gynoecium. Anthesis occur early in the morning and the petals present a ultraviolet reflection pattern. Solanum stramonifolium presents continuous flowering pattern and have hermaphrodite (62%) and functional male flowers (38%), therefore the species is andromonoicious. Thirteen species of bees were observed visiting the flowers of S. stramonifolium (nine pollinators and four pollen robbers). The great and constant production of flowers of S. stramonifolium along the year is important to maintain the pollinators guild and to guarantee the plant reproduction