Adaptive conduction delays and phase locking in spiking Haken Lighthouse networks.

Abstract

We develop a theory of phase-locked activity in delayed spiking networks using the Haken Lighthouse model as an analytically tractable event-based description of neural dynamics. For networks with fixed delays, we derive self-consistency conditions for phase-locked states and an associated linear stability theory formulated directly in terms of spike-time perturbations. The framework is illustrated for a delayed autapse, a reciprocally coupled two-cell network, and spatially structured rings with distance-dependent coupling and conduction delays, where circulant symmetry allows stability to be decomposed into Fourier modes. We then introduce an activity-dependent white matter plasticity rule in which myelination modulates axonal conduction speed and hence communication delay. This leads naturally to a slow-fast system with state-dependent delays, in which frozen phase-locked branches organise the adaptive dynamics. The plasticity rule selects commensurate delay-period relationships, providing a mechanism for the emergence of synchrony, other frequency-locked states, slow switching between competing phase-locked patterns, and the organisation of heterogeneous delays into discrete delay-period classes. Direct simulations of the event-driven network support the analytical predictions and illustrate how adaptive conduction can reshape the attractor structure of a delayed spiking network and generate long-timescale transitions. These results provide a tractable mathematical framework for studying how activity-dependent myelination may regulate temporal coordination, synchrony, and communication through coherence in spiking neural systems.