Quasiperiodic-Chaotic Neural Networks and Short-Term Analog Memory

Abstract

A model of quasiperiodic-chaotic neural networks is proposed on the basis of chaotic neural networks. A quasiperiodic-chaotic neuron exhibits quasiperiodic dynamics that an original chaotic neuron does not have. Quasiperiodic and chaotic solutions are exclusively isolated in the parameter space. The chaotic domain can be identified by the presence of a folding structure of an invariant closed curve. Using the property that the influence of perturbation is conserved in the quasiperiodic solution, we demonstrate short-term visual memory in which real numbers are acceptable for representing colors. The quasiperiodic solution is sensitive to dynamical noise when images are restored. However, the quasiperiodic synchronization among neurons can reduce the influence of noise. Short-term analog memory using quasiperiodicity is important in that it can directly store analog quantities. The quasiperiodic-chaotic neural networks are shown to work as large-scale analog storage arrays. This type of analog memory has potential applications to analog computation such as deep learning.