Inter-layer propagation of spiral waves: Effects of time-varying defect blocks and magnetic flows

Abstract

The variation of magnetic flux with distance and time is relatively common in nature. This paper investigates the inter-layer propagation of spiral waves in bi-layer Hindmarsh-Rose networks under gradient magnetic field and defect blocks motion, with the following conclusions: (1) Magnetic flux slows down the propagation of waves. (2) For defect blocks moving linearly or away from each other, spiral waves appear in the network, while the magnetic flux suppresses the spiral wave formation. (3) For defect blocks close to or merging with each other, the magnetic flow can only convert spiral waves in the network into “eye-like waves”. These findings imply that the propagation of spiral waves is sensitive to the action site of magnetic flux, which may be important for scar tissue (e.g., cardiac tissue with poor postoperative recovery). Moreover, three statistical parameters defined to detect waveform evolution in excitable media show good performance.