Spontaneous mode switching in coupled oscillators competing for constant amounts of resources.

We propose a widely applicable scheme of coupling that models competitions among dynamical systems for fixed amounts of resources. Two oscillators coupled in this way synchronize in antiphase. Three oscillators coupled circularly show a number of oscillation modes such as rotation and partially in-phase synchronization. Intriguingly, simple oscillators in the model also produce complex behavior such as spontaneous switching among different modes. The dynamics reproduces well the spatiotemporal oscillatory behavior of a true slime mold Physarum, which is capable of computational optimization.