Two reasons for the appearance of pushed wavefronts in the Belousov-Zhabotinsky system with spatiotemporal interaction

We prove the existence of the minimal speed of propagation c(*)(r, b, K) is an element of [2 root 1 - r, 2] for wavefronts in the Belousov-Zhabotinsky system with a spatiotemporal interaction defined by the convolution with (possibly, fat-tailed) kernel K. The model is assumed to be monostable non-degenerate, i.e. r is an element of (0, 1). The slowest wavefront is termed pushed or nonlinearly determined if its velocity c(*)(r, b, K) > 2 root/1 - r. We show that c(*)(r, b, K) is close to 2 if i) positive system's parameter b is sufficiently large or ii) K is spatially asymmetric to one side (e.g. to the left: in such a case, the influence of the right side concentration of the bromide ion on the dynamics is more significant than the influence of the left side). Consequently, this reveals two reasons for the appearance of pushed wavefronts in the Belousov-Zhabotinsky reaction. (c) 2023 Elsevier Inc. All rights reserved.

Automated summary

This study proves the existence of minimal propagation speed for wavefronts in the Belousov-Zhabotinsky system with spatiotemporal interaction defined by the kernel function K. The model assumes non-degenerate monostability and shows that the slowest wavefront is pushed or nonlinearly determined under certain conditions. The findings suggest that large positive system parameter b or spatial asymmetry in the kernel K contribute to the appearance of pushed wavefronts.