: Oscillation synchronization through diffusion-based communication of active materials can lead to emergence of diverse patterns and collective behaviors. A detailed general description of the formation process of synchronization or resynchronization dynamics is a challenging task. We employ a photosensitive Belousov-Zhabotinsky reaction-diffusion model (within a gel media) to investigate the recovery process of oscillation synchronization between a pair of gel patches. The recovery time for oscillation resynchronization can be modulated by patch-distance, species of signaling molecules, intensity and duration of illumination. Analysis reveals that the “switch effect” of the gel-distance and the “promotion effect” from illumination on the oscillation resynchronization originate from the competition between processes of photo-promotion of oscillation, diffusion of signaling molecules (HBrO2 and Br-) and disproportionation of HBrO2. These results will benefit studies on bio-inspired active materials and soft motors.

This paper aims to unify q-derivative/q-integral and h-derivative/h-integral in a single definition, this will be called q−h-derivative/q−h-integral. These notions are further extended on finite interval [a,b] in the form of left and right q−h-derivatives and q−h-integrals. Some inequalities are studied for q−h-integrals which are directly connected with well known results. In diverse fields of science and engineering the theory based on q-derivatives/q-integrals and h-derivatives/h-integrals can be unified by using the concept of q−h-derivative/q−h-integral.