  Systems with a complex dynamics like glasses or models of biological
evolution are often pictured in terms of complex landscapes, with a large
number of possible collective states. We show on the example of a stochastic
spin model with non-reciprocal and heterogeneous interactions how the complex
landscape notion can be generalized far from equilibrium, where collective
states may exhibit spontaneous oscillations, often hidden by the presence of
disorder. We identify relevant observables, like the density of entropy
production, to unveil the presence of oscillations, and we characterize the
complex landscape of our model in terms of a configurational entropy, that
counts the number of nonequilibrium collective states with a given entropy
production density.
