To communicate, an animal's strategic timing of rhythmic signals is crucial. Evolutionary, game-theoretical, and dynamical systems models can shed light on the interaction between individuals and the associated costs and benefits of signalling at a specific time. Mathematical models that study rhythmic interactions from a strategic or evolutionary perspective are rare in animal communication research. But new inspiration may come from a recent game theory model of how group synchrony emerges from local interactions of oscillatory neurons. In the study, the authors analyse when the benefit of joint synchronization outweighs the cost of individual neurons sending electrical signals to each other. They postulate there is a benefit for pairs of neurons to fire together and a cost for a neuron to communicate. The resulting model delivers a variant of a classical dynamical system, the Kuramoto model. Here, we present an accessible overview of the Kuramoto model and evolutionary game theory, and of the 'oscillatory neurons' model. We interpret the model's results and discuss the advantages and limitations of using this particular model in the context of animal rhythmic communication. Finally, we sketch potential future directions and discuss the need to further combine evolutionary dynamics, game theory and rhythmic processes in animal communication studies.