EXTINCTION OF OSCILLATION IN A REACTION-DIFFUSION SYSTEM

We have numerically studied a phenomenon, ''the extinction of oscillat ion'', in a reaction-diffusion system; all the oscillators stop togeth er in a limited region of the system size. In the numerical experiment s, we adopted a model of the van der Pol oscillator with or without pa cemakers. We found that the extinction of oscillation occurs when the size of the system N is comparatively small. In order to explain the n umerical results for the case of no pacemakers. we have developed a th eory for the system with the van der Pol oscillators, in which the Dir ichlet boundary condition is satisfied. The theory predicts that the s ystem breaks out, extincting the oscillation as expected, when the siz e of the system N corresponds to a critical size N-c and the oscillato rs never oscillate for a size N smaller than N-c. The theory also succ essfully explains the oscillating pattern and its maximum amplitude of the oscillation in the region of a system size larger than N-c.