Spiral waves on excitable media strongly influence the functions of living systems in both a positive and negative way. The spiral formation mechanism has thus been one of the major themes in the field of reaction-diffusion systems. Although the widely believed origin of spiral waves is the interaction of traveling waves, the heterogeneity of an excitable medium has recently been suggested as a probable cause. We suggest one possible origin of spiral waves using a Belousov-Zhabotinsky reaction and a discretized FitzHugh-Nagumo model. The heterogeneity of the reaction field is shown to stochastically generate unidirectional sites, which can induce spiral waves. Furthermore, we found that the spiral wave vanished with only a small reduction in the excitability of the reaction field. These results reveal a gentle approach for controlling the appearance of a spiral wave on an excitable medium.

For many gastropods, locomotion is driven by a succession of periodic muscular waves (contractions and relaxations) moving along the foot. The force generated by these waves is coupled to the substratum by a thin layer of pedal mucus. Gastropod pedal mucus has unusual physical properties: the mucus is a viscoelastic solid at small deformation and shows a sharp yield point; then, at greater strains, the mucus is a viscous liquid, although it will recover its solidity if allowed to heal for a certain period. In this paper, to clarify the role of the mucus and the flexible muscular waves in adhesive locomotion, we use a simple mathematical model to verify that directional migration can be realized through the interaction between the periodic muscular waves and the specific physical features of mucus. Our results indicate that the hysteresis property of mucus is essential in controlling kinetic friction for the realization of crawling locomotion. Furthermore, our numerical calculations show that both the hysteresis property of mucus and the contraction ratio of muscle give rise to two styles of locomotion, direct waves and retrograde waves, which until now have been explained by different mechanisms. The biomechanical effectiveness of mucus in adhesive locomotion is also discussed.

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