Abstract
Diverse spatiotemporal patterns are generated in a three-variable reaction-diffusion model that supports 1(1) mixed-mode oscillations. Diffusion-induced instability results in spatiotemporal patterns such as amplitude-modulated overtargets (circular super-waves superimposed on spiral waves) and superspirals. The types of superstructure waves are determined by the ratio of diffusion coefficients, which controls the interaction and competition between two local oscillatory modes, one of which is the original homogeneous 1(1) mixed-mode oscillation, resulting in periodic amplitude modulation in space. Variation of the control parameter can reverse the chirality and radial propagation direction (outward or inward rotation) of a superspiral pattern. These amplitude-modulated patterns may provide insight into mechanisms of pattern development in some living systems.