Memorization and prediction capability of the interacting phase oscillators

Abstract

Nonlinear dynamical systems, such as well-tuned recurrent neural networks, have proved a powerful tool for modeling temporal data. However, tuning such models to achieve optimal performance remains an outstanding challenge, not least because of the complex behaviors that emerge from interacting microscopic constituents. Here, we consider a minimal model of two interacting phase oscillators coupled to a thermal bath and driven by a common signal. We quantify the memory and predictive capability of the system with the mutual information between the phases of oscillators and the signals at different times. We show that the interaction between oscillators can increase the information between the system and the movement. We attribute this behavior to an increase in the effective signal-to-noise ratio, resulting from a stronger correlation between the oscillators. We also demonstrate that heterogeneity in the natural frequencies of the oscillators can further increase the mutual information though more efficient uses of oscillator states.Our work offers the first step toward a systematic approach to optimizing interacting nonlinear dynamical systems for memorizing and predicting temporal patterns.