Rotating Wave Dynamics in Rings of Coupled Oscillators: Insights into Working Memory Models

This paper explores rotating waves, a captivating synchronization phenomenon observed in interconnected oscillators. These waves emerge from phase differences between neighboring oscillators, giving rise to stable periodic, quasiperiodic, or chaotic orbits. Rotating waves are observed in diverse non-linear systems like electrical circuits, neural models, and various oscillators. The study employs techniques such as time series and phase-space analyses, bifurcation diagrams, power spectra, and basins of attraction to unveil the intricate dynamics. These methods reveal the route from stable equilibria to hyperchaos through a series of bifurcations with increasing coupling strength, including Andronov-Hopf, torus, and crisis bifurcations. Notably, the research identifies instances of multiple coexisting rotating waves under the same parameters. Special attention is given to neural oscillators due to their significance in brain neural rings associated with working memory. The study of rotating waves finds broad relevance in fields like lasers, chemical reactions, cardiorespiratory systems, and particularly neural networks and brain function.