An amoeboid organism, the true slime mold Physarum, has been studied actively in recent years to explore its spatiotemporal oscillatory dynamics and various computational capabilities. In the authors' previous studies, the amoeba was employed as a computing substrate to construct a neurocomputer. Under optical feedback control to implement a recurrent neural network model, the amoeba grows or withdraws its photosensitive branches by exhibiting a number of spatiotemporal oscillation modes in search of a solution to some combinatorial optimization problems. In this paper, considering the amoeba as a network of oscillators that compete for constant amounts of resources, we model the amoeba-based neurocomputer. The model generates several oscillation modes and produces not only simple behavior to stabilize a single mode but also complex behavior to spontaneously switch among different modes. To explore significances of the oscillatory dynamics in producing the computational capabilities, we establish a test problem that is a kind of optimization problem of how to allocate a limited amount of resource to oscillators so that conflicts among theoscillators can be avoided. We compare the performances of the oscillation modes in solving the problem in a bottom-up manner.