Nonequilibrium connectivity transitions and hysteretic recovery in threshold-gated mobile temporal networks

Threshold-gated interactions can change not only when connectivity is lost in a noise-driven mobile network, but also how it is recovered. We study a threshold-gated temporal network of mobile agents in which geometrically admissible pairwise interactions become active only when the instantaneous channel quality exceeds a prescribed threshold. The resulting temporal graph depends jointly on communication state and agent motion. To represent the feedback from maneuvering to link reliability, we introduce a phenomenological motion-induced self-noise term, which is equivalent to raising the effective threshold of near-threshold links during strong commanded reorientation. Using the largest weakly connected component as the connectivity order parameter S, and interpreting the finite-size diagnostics as effective finite-size descriptors, we identify pseudo-critical fluctuations, finite-size-dependent crossover behavior, topology–dynamics decoupling, and hysteresis under the employed parameter-sweep protocol. Control comparisons show that local motion–communication feedback is reflected in recovery-branch displacement, collapse–recovery pathway modification, penalty-generation diagnostics, and fragmented-state temporal organization, rather than in a single scalar loop metric. Hysteresis area and maximum branch gap are scalar measures of loop magnitude rather than direct evidence of feedback locality, and long fragmented-state residence events can also be modified by nonlocal or externally imposed penalty terms. Within the full local-feedback family, increasing feedback strength increases fragmented-state occupancy, promotes frequent brief visits to the fragmented branch, and makes rare long disconnection events more accessible. Although weak underwater communication provides the immediate physical motivation, the formulation is cast at the level of threshold-activated, intermittently interacting, and state-dependent mobile temporal networks, and therefore applies more broadly to mobile dynamical systems with directional and state-dependent interactions.