Bifurcation analysis of a new Lorenz-like chaotic system

In this paper we study the local codimension one and two bifurcations which occur in a family of three-dimensional vector fields depending on three parameters. An equivalent family, depending on five parameters, was recently proposed as a new chaotic system with a Lorenz-like butterfly shaped attractor and was studied mainly from a numerical point of view, for particular values of the parameters, for which computational evidences of the chaotic attractor was shown. In order to contribute to the understand of this new system we present an analytical study and the bifurcation diagrams of an equivalent three parameter system, showing the qualitative changes in the dynamics of its solutions, for different values of the parameters. (C) 2007 Elsevier Ltd. All rights reserved.

Dynamics at infinity and the existence of singularly degenerate heteroclinic cycles in the Lorenz system

In this paper, by using the Poincare compactification in R(3) we make a global analysis of the Lorenz system, including the complete description of its dynamic behavior on the sphere at infinity. Combining analytical and numerical techniques we show that for the parameter value b = 0 the system presents an infinite set of singularly degenerate heteroclinic cycles, which consist of invariant sets formed by a line of equilibria together with heteroclinic orbits connecting two of the equilibria. The dynamical consequences related to the existence of such cycles are discussed. In particular a possibly new mechanism behind the creation of Lorenz-like chaotic attractors, consisting of the change in the stability index of the saddle at the origin as the parameter b crosses the null value, is proposed. Based on the knowledge of this mechanism we have numerically found chaotic attractors for the Lorenz system in the case of small b > 0, so nearby the singularly degenerate heteroclinic cycles.

GLOBAL DYNAMICS of THE LORENZ SYSTEM WITH INVARIANT ALGEBRAIC SURFACES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Reproductive biology of the smooth butterfly ray Gymnura micrura

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

Protandry and female size-fecundity variation in the tropical butterfly Brassolis sophorae

Protandry (the emergence of males before fe males) is currently explained either as a mating strategy to maximize number of matings in the males, or a way to minimize pre-reproductive mortality in females, Models of protandry have generally ignored variation in female quality (reproductive potential). We recorded the sex ratio, female body mass, wing length and potential fecundity (number and mass of eggs) of the tropical butterfly Brassolis sophorae through the emergence period. Temporal variation in female size and fecundity correlated with male potential for acquiring mates. Females from the end of the emergence period showed lower fecundity and size. Males emerging before and close to the median date of the female emergence period had greater mating opportunities. Males emerging either very early or late were penalized by few mating opportunities, or by encounters with small: low-quality females, respectively.

A controller design used in Lorenz synchronization chaotic system for secure communication based on LMI fuzzy control system

This paper describes a mathematical study about chaotic system and about the unified approach of chaos control via fuzzy control system based in Linear Matrix Inequality to design a controller which synchronizes the transmission/reception system. This system, that was based in Lorenz chaotic circuit, can be used for transmit signals in secure way.

Divergences of generalized quantum electrodynamics on the Lorenz gauge

In this paper we study the Generalized Quantum Electrodynamics (GQED4) on the Lorenz gauge condition and show that divergences are still present in the theory. © 2013 American Institute of Physics.

Diet and feeding strategy of smooth butterfly ray Gymnura micrura in northeastern Brazil

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