Collective behavior of higher-order globally coupled oscillatory networks in response to positive and negative couplings.

Collective behavior is among the most fascinating complex dynamics in coupled networks with applications in various fields. Recent works have shown that higher-order interactions widely exist in complex systems. Both positive couplings among nodes, as the majority of studies have assumed, and negative couplings are very common in real-world systems, like physiological networks. Positive coupling (excitatory coupling) promotes synchronization and drives excitatory synaptic transmission between neurons. Meanwhile, negative coupling (inhibitory coupling) inhibits synchronization and sustains inhibitory synaptic transmission between neurons. Since high-order coupling patterns and different coupling patterns strongly affect the synchronous performance of complex systems, this article develops a globally coupled higher-order oscillatory system model that incorporates both positive and negative couplings. It is shown that, in the case of positive couplings, a second-order interaction has a negligible impact on the synchronization capability of a network within a certain range. In contrast, a higher-order network with purely negative couplings exhibits asynchronous states for any values of the second-order interactions. However, the synchronous region gradually shrinks with the increase of the negative coupling in the case of mixed couplings. This indicates a prominent role of coupling patterns on the onset of globally higher-order network synchronization.