Adapting to regularities of the environment is critical for biological organisms to anticipate events and plan. A prominent example is the circadian rhythm corresponding to the internalization by organisms of the $24$-hour period of the Earth’s rotation. In this work, we study the emergence of circadian-like rhythms in deep reinforcement learning agents. In particular, we deployed agents in an environment with a reliable periodic variation while solving a foraging task. We systematically characterize the agent’s behavior during learning and demonstrate the emergence of a rhythm that is endogenous and entrainable. Interestingly, the internal rhythm adapts to shifts in the phase of the environmental signal without any re-training. Furthermore, we show via bifurcation and phase response curve analyses how artificial neurons develop dynamics to support the internalization of the environmental rhythm. From a dynamical systems view, we demonstrate that the adaptation proceeds by the emergence of a stable periodic orbit in the neuron dynamics with a phase response that allows an optimal phase synchronisation between the agent’s dynamics and the environmental rhythm.

The time-delay-based reservoir computing setup has seen tremendous success in both experiment and simulation. It allows for the construction of large neuromorphic computing systems with only few components. However, until now the interplay of the different timescales has not been investigated thoroughly. In this manuscript, we investigate the effects of a mismatch between the time-delay and the clock cycle for a general model. Typically, these two time scales are considered to be equal. Here we show that the case of equal or resonant time-delay and clock cycle could be actively detrimental and leads to an increase of the approximation error of the reservoir. In particular, we can show that non-resonant ratios of these time scales have maximal memory capacities. We achieve this by translating the periodically driven delay-dynamical system into an equivalent network. Networks that originate from a system with resonant delay-times and clock cycles fail to utilize all of their degrees of freedom, which causes the degradation of their performance.