A Network of Neural Oscillators for Fractal Pattern Recognition

Abstract

Biological neural networks are high dimensional nonlinear systems, which presents complex dynamical phenomena, such as chaos. Thus, the study of coupled dynamical systems is important for understanding functional mechanism of real neural networks and it is also important for modeling more realistic artificial neural networks. In this direction, the study of a ring of phase oscillators has been proved to be useful for pattern recognition. Such an approach has at least three nontrivial advantages over the traditional dynamical neural networks: 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 were 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. We manipulate the number of neurons and initial conditions of the oscillator ring to encode fractal patterns. It is worth noting that fractal pattern recognition is a challenging problem due to their discontinuity nature and their complex forms. Computer simulations confirm good performance of the proposed algorithms.