Nonmonotonic control of pattern formation by chemotaxis

We investigate pattern formation in generic two-species reaction–diffusion systems with chemotaxis. We show that chemotaxis can give rise to a striking nonmonotonic dependence of pattern formation on its strength, opening the possibility of re-entrant transitions between patterned and homogeneous states controlled by chemotaxis. 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.