Abstract
The influence of long-range links on spiral waves in an excitable medium has been investigated. Spatiotemporal dynamics in an excitable small-world network transform remarkably when we increase the long-range connection probability P. Spiral waves with few perturbations, broken spiral waves, pseudo spiral turbulence, synchronous oscillations, and homogeneous rest state are discovered under different network structures. Tip number is selected to detect non-equilibrium phase transition between different spatiotemporal patterns. The Kuramoto order parameter is used to identify these patterns and explain the emergence of the rest state. Finally, we use long-range links to successfully control spiral waves and spiral turbulence.