Resonances and subharmonic bifurcations of large amplitude periodic orbits of planar polynomial vector fields

In this work are studied periodic perturbations, depending on two parameters, of planar polynomial vector fields having an annulus of large amplitude periodic orbits, which accumulate on a symmetric infinite heteroclinic cycle. Such periodic orbits and the heteroclinic trajectory can be seen only by the global consideration of the polynomial vector fields on the whole plane, and not by their restriction to any compact set. The global study involving infinity is performed via the Poincare Compactification. It is shown that, for certain types of periodic perturbations, one can seek, in a neighborhood of the origin in the parameter plane, curves C-(m) of subharmonic bifurcations, for which the periodically perturbed system has subharmonics of order m, for any integer m.

Periodic perturbations of quadratic planar polynomial vector fields

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Large amplitude oscillations for a class of symmetric polynomial differential systems in R³

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Multidimensional polynomial powers of sigmoid (PPS) Wavelet neural networks

Wavelet functions have been used as the activation function in feedforward neural networks. An abundance of R&D has been produced on wavelet neural network area. Some successful algorithms and applications in wavelet neural network have been developed and reported in the literature. However, most of the aforementioned reports impose many restrictions in the classical backpropagation algorithm, such as low dimensionality, tensor product of wavelets, parameters initialization, and, in general, the output is one dimensional, etc. In order to remove some of these restrictions, a family of polynomial wavelets generated from powers of sigmoid functions is presented. We described how a multidimensional wavelet neural networks based on these functions can be constructed, trained and applied in pattern recognition tasks. As an example of application for the method proposed, it is studied the exclusive-or (XOR) problem.

Human face verification based on multidimensional Polynomial Powers of Sigmoid (PPS)

In this paper, we described how a multidimensional wavelet neural networks based on Polynomial Powers of Sigmoid (PPS) can be constructed, trained and applied in image processing tasks. In this sense, a novel and uniform framework for face verification is presented. The framework is based on a family of PPS wavelets,generated from linear combination of the sigmoid functions, and can be considered appearance based in that features are extracted from the face image. The feature vectors are then subjected to subspace projection of PPS-wavelet. The design of PPS-wavelet neural networks is also discussed, which is seldom reported in the literature. The Stirling Universitys face database were used to generate the results. Our method has achieved 92 % of correct detection and 5 % of false detection rate on the database.