| Abstract: |
| In reaction diffusion system, we can observe non-uniform patterns induced by Turing instability or wave instability, which are well-known mechanisms for pattern formation. These instabilities can be also considered as global feedback to an activator. However, in experiment, there is reaction diffusion system with feedback to an inhibitor. Especially, in the photosensitive Belousov-Zhabotinsky (BZ) reaction system, several oscillatory cluster patterns such as standing wave are observed by inhibitory global feedback effect. Meanwhile, we can observe antiphase-like patterns such as standing wave through numerical simulation of the Oregonator model, which is a famous mathematical model for the BZ reaction, with global feedback to the inhibitor. However, we have not sufficiently understood the structure for appearance of the oscillatory cluster pattern. Thus, in this study, we investigated the simple situation such as the coupled oscillator system because this system can be considered as the simplest situation of the oscillatory spatial pattern. We located the bifurcational origin for some oscillatory patterns using numerical simulation. In particularly, the bifurcation structure is changed by the competition between diffusion and feedback. Moreover, we confirmed that this theoretical result was consistent with the experiment of the photosensitive BZ reaction. |
|