Patterns of neuronal synchrony in higher-order networks.

Synchrony in neuronal networks is crucial for cognitive functions, motor coordination, and various neurological disorders. While traditional research has focused on pairwise interactions between neurons, recent studies highlight the importance of higher-order interactions involving multiple neurons. Both types of interactions lead to complex synchronous spatiotemporal patterns, including the fascinating phenomenon of chimera states, where synchronized and desynchronized neuronal activity coexist. These patterns are thought to resemble pathological states such as schizophrenia and Parkinson's disease, and their emergence is influenced by neuronal dynamics as well as by synaptic connections and network structure. This review integrates the current understanding of how pairwise and higher-order interactions contribute to different synchrony patterns in neuronal networks, providing a comprehensive overview of their role in shaping network dynamics. We explore a broad range of connectivity mechanisms that drive diverse neuronal synchrony patterns, from pairwise long-range temporal interactions and time-delayed coupling to adaptive communication and higher-order, time-varying connections. We cover key neuronal models, including the Hindmarsh-Rose model, the stochastic Hodgkin-Huxley model, the Sherman model, and the photosensitive FitzHugh-Nagumo model. By investigating the emergence and stability of various synchronous states, this review highlights their significance in neurological systems and indicates directions for future research in this rapidly evolving field.