  Multifunctional neural networks are capable of performing more than one task
without changing any network connections. In this paper we explore the
performance of a continuous-time, leaky-integrator, and next-generation
`reservoir computer' (RC), when trained on tasks which test the limits of
multifunctionality. In the first task we train each RC to reconstruct a
coexistence of chaotic attractors from different dynamical systems. By moving
the data describing these attractors closer together, we find that the extent
to which each RC can reconstruct both attractors diminishes as they begin to
overlap in state space. In order to provide a greater understanding of this
inhibiting effect, in the second task we train each RC to reconstruct a
coexistence of two circular orbits which differ only in the direction of
rotation. We examine the critical effects that certain parameters can have in
each RC to achieve multifunctionality in this extreme case of completely
overlapping training data.
