Pacemaker-induced spiral wave chimeras on a sphere of delay-coupled oscillators: Switching between different spiral-phase kinks.

Two-dimensional systems of nonlocally coupled oscillators exhibit spiral wave chimeras, a phenomenon that has garnered significant attention in nonlinear dynamics. These chimeras are characterized by the simultaneous presence of synchronized spiral regions and desynchronized phase-randomized cores. In contrast, biological pacemakers have been shown to entrain organic cells, producing regular rhythmic patterns. Here, we report on a rather surprising finding that the spiral chimeras emerge from a spatially homogeneous state due to an external pacemaker in a sphere of all-to-all coupled oscillators interacting with distance-dependent time delays. Our results reveal that the emergent spiral chimeras exhibit an exotic type of dynamics that presents the spiral arms with phase kinks. Notably, our analysis demonstrates that such a kink-spiral chimera state is universally observed in both pure-phase and amplitude-phase oscillator systems. Moreover, we show that adjusting the forcing strength and frequency of the pacemaker enables the switching between multiple types of kink-spiral chimeras. Furthermore, for the phase oscillator system, we uncover the intricate structure of the Arnold tongue, illustrating a resonant-type interplay between the pacemaker's frequency and interaction time delay that governs spiral chimera formation. This study sheds light on the dynamics of coupled oscillators and highlights the role of external drivers in generating complex spatiotemporal patterns.