Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 3

In this paper, we classify all the global phase portraits of the quadratic polynomial vector fields having a rational first integral of degree 3. (C) 2008 Elsevier Ltd. All rights reserved.

Reproductive biology of six Brazilian Myrtaceae: is there a syndrome associated with buzz-pollination?

The floral phenology and reproductive biology of six sympatric arboreal Myrtaceae species were studied in the coastal plain forest (Ubatuba, Brazil, 44 degrees 48`W 23 degrees 22`S), from September 1999 to April 2002. Flowering started in the transition from the driest to the most humid season (Sep/Oct) and lasted until March. The sequence with which the species flowered each year was consistently the same. However, the timing of flowering onset, peak, end, and overlap differed from one year to another. Myrtaceae species were classified as xenogamic according to the pollen:ovule ratios, but two of them seem to present some degree of self-compatibility. Flowers of all species opened at sunrise and lasted for I day. Bombus morio (Apidae: Bombini) was the most common visitor followed by Melipona rufiventris (Apidae: Meliponini). Buzz pollination in Myrtaceae was common at the study area and seems to be related to bees` behaviour and to some aspects of flowers` morphology.