Basins of Attraction for Partial Synchronization States in Locally Coupled Neuronal Systems

The basin of attraction is one of the most fundamental concepts in modern dynamical systems theory. However, its definition for spatially extended systems, particularly those capable of supporting a wide spectrum of partial synchronization states, remains challenging. In this paper, we analyze a neuronal network that is simple in a configurational sense, developing full and partial synchronization states from specially structured large-scale periodic initial conditions. This approach allows restructuring the basin of attraction within a lower-dimensional space and examine its structure comprehensively. Given the empirically established link between cortical waves, partial synchronization states, and information processing in cortical structures, this study may contribute to a fundamental understanding of functional zone dynamics from the perspective of dynamical systems theory. It may also reveal the coordination mechanisms mediated by effective connectivity.