Re-entrance or monotonic: How chemotaxis controls pattern formation

Abstract

We investigate pattern formation in generic two-species reaction-diffusion systems with mutual chemotaxis. We show that tuning the chemotaxis strength can give rise to striking nonmonotonic variation of patterns, opening the possibility of re-entrant transitions between patterned and spatially uniform steady states. In certain regimes, chemotaxis also induces additional heretofore unexplored instabilities. Furthermore, varying the strength of chemotaxis can drive morphological transitions between spot and stripe patterns.

Final version