Emergence of self-sustained patterns in small-world excitable media

Abstract

Motivated by recent observations that long-range connections (LRC) play a role in various brain phenomena, we have observed two distinct dynamical transitions in the activity of excitable media where waves propagate both between neighboring regions and through LRC. When LRC density $p$ is low, single or multiple spiral waves are seen to emerge and cover the entire system. This state is self-sustaining and robust against perturbations. At $p=p_c^l$ the spirals are suppressed and there is a transition to a spatially homogeneous, temporally periodic state. Finally, above $p=p_c^u$, activity ceases after a brief transient.

4 pages, 5 figures

References in corpus (1)

• Scale-free brain functional networks

Cited by in corpus (4)

• Effect of small-world topology on wave propagation on networks of excitable elements
• Multistability, local pattern formation, and global collective firing in a small-world network of non-leaky integrate-and-fire neurons
• Excitation Waves on a Minimal Small-World Model
• Memory-induced mechanism for self-sustaining activity in networks