Recognizing Fractal Patterns Using a Ring of Phase Oscillators

A ring of phase oscillators has been proved to be useful for pattern recognition. It has at least three nontrivial advantages over the traditional dynamical neural networks, such as Hopfield Model: First, each input pattern can be encoded in a vector instead of a matrix, second, the connection weights can be determined analytically, third, due to its dynamical nature, it has the ability to capture temporal patterns. In the previous studies of this topic, all patterns are encoded as stable periodic solutions of the oscillator network. In this paper, we continue to explore the oscillator ring for pattern recognition. Specifically, we propose algorithms, which use the chaotic dynamics of the closed loops of Stuart-Landau Oscillators as artificial neurons, to recognize randomly generated fractal patterns. It is worth to note that fractal pattern recognition is a challenge problem due to their discontinuity nature and their complex form.