Storage and recall of multiple chaotic attractors in minimal reservoir computers

Modern predictive modeling increasingly calls for a single learned dynamical substrate to operate across multiple regimes. From a dynamical systems viewpoint, this capability decomposes into the storage of multiple attractors and the recall of the appropriate attractor in response to contextual cues. In reservoir computing, multi-attractor learning has largely been pursued using large, randomly wired reservoirs, on the assumption that stochastic connectivity is required to generate sufficiently rich internal dynamics. At the same time, recent work shows that minimal deterministic reservoirs can match random designs for single-system chaotic forecasting. In this paper, we examine the conditions under which minimal reservoir topologies can learn multiple chaotic attractors across storage and recall settings. Using a storage and recall protocol, we find that minimal architectures struggle when explicit recall is required. We then introduce an input concatenation training strategy, in which two attractors are embedded into a single enlarged input space, and show that these reservoirs can represent the joint evolution of multiple chaotic attractors. We test all 28 unordered system pairs formed from eight three-dimensional chaotic systems. Across the ten deterministic topologies investigated, we do not observe a robust dependence of multi-attractor performance on reservoir topology: No single topology consistently outperforms the others in either the storage-only or cue-dependent recall settings. Our results indicate that minimal reservoirs can learn multiple attractors when they are presented jointly but struggle to reliably recall a specific attractor from a model trained on multiple systems.