We perform a numerical study of the trajectories of spiral wave cores in excitable systems whose excitability is modulated in proportion to the integral of the activity in a sensory domain in the shape of an equilateral triangle. As a result of this domain shape having vertices opposite sides, unusual forms of lobed limit cycles occur, which are destroyed and then re-form as the domain size is varied. Some key results are also demonstrated experimentally using the light-sensitive Belousov-Zhabotinsky reaction. To characterize the observed behavior, we introduce the concept of express and stagnation zones, which are regions where the trajectory moves particularly rapidly or slowly. The location and strength of the zones far from the domain are accounted for by approximating the parts of the spiral wave crossing the domain by a series of plane waves.