Building mathematical models of brains is difficult because of the sheer complexity of the problem. One potential starting point is through basal cognition, which gives abstract representation of a range of organisms without central nervous systems, including fungi, slime moulds and bacteria. We propose one such model, demonstrating how a combination of oscillatory and current-based reinforcement processes can be used to couple resources in an efficient manner, mimicking the way these organisms function. A key ingredient in our model, not found in previous basal cognition models, is that we explicitly model oscillations in the number of particles (i.e. the nutrients, chemical signals or similar, which make up the biological system) and the flow of these particles within the modelled organisms. Using this approach, we find that our model builds efficient solutions, provided the environmental oscillations are sufficiently out of phase. We further demonstrate that amplitude differences can promote efficient solutions and that the system is robust to frequency differences. In the context of these findings, we discuss connections between our model and basal cognition in biological systems and slime moulds, in particular, how oscillations might contribute to self-organised problem-solving by these organisms.