Generalizing layered sequential control to arbitrary multi‑attractor networks

Demonstrate that the layered threshold‑linear network architecture for internally encoding sequences of dynamic attractors—comprising a CTLN counter layer (L1), an intermediate relay layer (L2), and a multi‑attractor CTLN layer (L3)—works when L3 is replaced by any network that has coexistent attractors accessible via changes in initial conditions or targeted stimulation. Establish necessary and sufficient conditions under which such sequences can be reliably generated using identical pulses to L1/L2.

Background

The dissertation constructs layered networks to internally encode sequences of dynamic attractors by combining a counter in L1, a relay in L2, and a multi-attractor module in L3 (quadruped gaits or Clione’s hunting network). Pulses to L1/L2 activate specific attractors in L3 according to fixed wiring, achieving flexible sequencing without changing parameters within L3.

The authors conjecture this mechanism could generalize beyond the two demonstrated CPGs, suggesting broader applicability to any multi‑attractor network accessible via initial conditions or targeted stimulation. A general proof and precise conditions for such generalization remain to be established.