The present work systematically examines the effect of breaking the rotational symmetry of a surface on the spot positioning in reaction-diffusion (RD) systems. In particular, we study analytically and numerically the steady-state positioning of a single spot in RD systems on a prolate and an oblate ellipsoid. We adapt perturbative techniques to perform a linear stability analysis of the RD system on both ellipsoids. Furthermore, the spot positionings in the steady states of non-linear RD equations are obtained numerically on both ellipsoids. Our analysis suggests that preferential spot positioning can be observed on non-spherical surfaces. The present work may provide useful insights into the role of cell geometry on various symmetry-breaking mechanisms in cellular processes.
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