Chimera states in coupled pendulum with higher-order interaction

The study of chimera states in non-pairwise interaction networks is one of the challenging issues in current research. In recent work [S. Kundu and D. Ghosh (2022)], it was discovered that higher-order interactions promote chimera states in nonlocally coupled identical Kuramoto oscillators. In this work, we investigate a higher-order interaction network of a nonlocally coupled pendulum with inertia. By studying pairwise and non-pairwise interaction strengths, we observe different collective states, like synchronization, coherent traveling waves, single-head, multi-head, imperfect traveling chimera states, and incoherent states. In particular, we discover a novel non-stationary chimera state, namely a penetrable traveling chimera state, where the oscillators in the coherent domain of the network travel regularly while others drift randomly in the incoherent domain. We make a map of all the spatiotemporal behaviors in the parameter space of interactive coupling and identify the transition from non-stationary chimeras to coherent states passing through stationary chimeras. As higher-order coupling strength increases, collective dynamics eventually transit to coherence since higher-order interactions are conducive to the emergence of a multi-stable state even without non-pairwise interactions, as demonstrated by the basin stability simulations. After analyzing the damping effects, we consolidate the generality of damping in eradicating dynamical behavior. The abundant dynamics appear, then deteriorate, and even disappear in the corresponding model with inertia. The study of rich dynamic behavior is essential for facilitating an understanding of the impact of higher-order interactions and damping effects on the dynamics of complex real-world networks.