Effect of network structural perturbations on spiral wave patterns

Dynamical patterns in complex networks of coupled oscillators are of both theoretical and practical interest, yet to fully reveal and understand the interplay between pattern emergence and network structure remains to be an open problem. Among the many outstanding issues, a fundamental one is how the network structure affects the stability of dynamical patterns. To address this issue, we focus on the spiral wave patterns and investigate the effects of systematically added random links on their stability and dynamical evolutions. We find that, as the network structure deviates more from the regular topology and thus becomes increasingly more complex, an originally stable spiral wave pattern can disappear but different types of patterns can emerge. In addition, short-distance links added to a small region containing the spiral tip can have a more significant effect on the wave pattern than long-distance connections. As more random links are introduced into the network, distinct pattern transitions can occur, such as the transition of the spiral wave pattern to a global synchronization state, to a chimera-like state, or to a pinned spiral wave. About the transition points, the network dynamics are highly sensitive to small structural perturbations in that the addition of even a single link can change the pattern from one type to another. These findings provide additional insights into the pattern dynamics in complex networks, a problem that is relevant to many physical, chemical, and biological systems.