Deterministic phase memory II: Global bifurcation structure and robustness

We construct cascades of N identical bistable phase-memory cells, producinga 2N-dimensional dynamical system that realizes an exponential memory archi-tecture. Building on the minimal bistable cell and explicit switching thresholdsestablished in Part I 1, we prove: (i) the existence of 2N asymptotically stableequilibria at weak coupling via persistence of hyperbolic equilibria; (ii) an explicitsucient bound on the coupling strength guaranteeing stability, with quantitativecontrol of the perturbation remainder; (iii) strong addressability: a write pulse ap-plied to the i-th cell switches it without causing any other cell to leave an explicitneighborhood of its equilibrium, even during the transient; (iv) a spectral analysisof the bidirectional cascade via block-tridiagonal Jacobian structure, showing thatdiusive coupling is unconditionally stabilizing. A concrete numerical example withβ = 2.5 and N = 8 illustrates the theory. This work is a preprint and has not yet been peer reviewed.