adaptive-conduction-delays-haken-lighthouse

name

adaptive-conduction-delays-haken-lighthouse

description

Adaptive conduction delays and phase locking in spiking Haken Lighthouse networks. Theory of phase-locked activity in delayed spiking networks using analytically tractable event-based neural dynamics. Introduces activity-dependent white matter plasticity with myelination-modulated axonal conduction speed. Activation: Haken Lighthouse, phase locking, conduction delays, myelin plasticity, spike-time perturbations, circulant symmetry, Fourier modes.

Methodology Overview

Analytically tractable theory of phase-locked activity in delayed spiking networks using the Haken Lighthouse model. Derives self-consistency conditions for phase-locked states and linear stability theory formulated directly in spike-time perturbations. Introduces activity-dependent myelination plasticity.

Key Innovation Points

1. Haken Lighthouse Model

   • Event-based description of neural dynamics
   • Analytically tractable (exact solutions possible)
   • Spike-time based framework
   • Phase dynamics approach to spiking networks

2. Delayed Network Theory

   • Self-consistency conditions for phase-locked states
   • Linear stability theory in spike-time perturbations
   • Fixed delay networks: analytical solutions
   • Distance-dependent coupling and conduction delays

3. Circulant Symmetry

   • Spatially structured ring networks
   • Fourier mode decomposition of stability
   • Distance-dependent delays
   • Ring topology with circulant structure

4. White Matter Plasticity Rule

   • Activity-dependent myelination
   • Modulates axonal conduction speed
   • Dynamic communication delays
   • Learning-based delay adaptation

Activation Keywords

• Haken Lighthouse model, event-based spiking
• Phase locking, phase-locked states
• Conduction delays, axonal delays
• Myelin plasticity, white matter plasticity
• Spike-time perturbations
• Circulant symmetry, Fourier modes
• Delayed autapse, reciprocally coupled networks
• Activity-dependent myelination

Technical Details

Haken Lighthouse Dynamics

Event-based formulation:
- Phase variable θ evolves continuously
- Spike occurs when θ reaches threshold
- Reset mechanism after spike
- Analytical solutions for fixed delays

Self-Consistency Conditions

For phase-locked states:
θ_i(t) = θ_0 + ω*t + φ_i
where φ_i satisfies:
φ_i = Σ_j W_ij * sin(φ_j - φ_i - τ_ij)

Stability Theory

Linear stability via spike-time perturbations:
δ(t) = Σ_n A_n * exp(λ_n * t)
where λ_n are eigenvalues of Jacobian

Myelination Plasticity Rule

Delay adaptation:
τ_ij → τ_ij - η * (activity - target)
Conduction speed proportional to myelin thickness
Activity-dependent white matter remodeling

Network Examples

1. Delayed Autapse

   • Single neuron with self-feedback
   • Fixed delay loop
   • Phase-locked solutions

2. Two-Cell Reciprocal Network

   • Two neurons with reciprocal coupling
   • Distance-dependent delays
   • Phase locking conditions

3. Ring Networks

   • N-neuron ring with circulant symmetry
   • Fourier mode decomposition
   • Stability analysis by modes

Biological Significance

Myelin Plasticity

• White matter adapts to activity patterns
• Axonal speed increases with usage
• Learning modifies communication delays
• Dynamic rewiring via myelination

Delay Adaptation Mechanism

• Activity → myelin thickness → conduction speed
• Local plasticity rule
• Global network reorganization
• Spike-timing dependent changes

Applications

1. Delayed Neural Networks

   • Phase locking analysis
   • Delay-based computation
   • Synchronization with conduction delays

2. White Matter Modeling

   • Activity-dependent myelination
   • Dynamic delay networks
   • Learning-induced connectivity changes

3. Spike-Time Perturbation Theory

   • Stability analysis framework
   • Event-based dynamics
   • Analytical tractability

4. Neuromorphic Engineering

   • Delay plasticity in hardware
   • Phase-based synchronization
   • Circulant architectures

Implementation Notes

Haken Lighthouse Model

θ'(t) = ω - Σ_j W_ij * δ(t - t_j - τ_ij)
where δ is Dirac delta (event-based)

Phase-Locked Solutions

Self-consistency equation:
φ_i = Σ_j W_ij * sin(φ_j - φ_i - τ_ij * ω)

Fourier Stability Analysis

For ring with N neurons:
λ_k = Σ_j W_j * cos(k * 2π/N) * exp(-λ_k * τ_j)
k = 0, 1, ..., N-1

Key Equations

Event-Based Dynamics

Spike time equation:
t_i^{n+1} = t_i^n + Δ where Δ = 2π/ω (baseline)
with perturbations from incoming spikes

Delay Perturbation

δτ_ij = -η * (r_ij - r_target)
where r_ij is activity on connection i→j

Stability Matrix

J_ij = W_ij * cos(φ_j - φ_i - τ_ij) for fixed delays
Eigenvalue problem for stability

Experimental Observations

• Phase locking emerges for appropriate delays
• Myelination speeds up high-activity pathways
• Plasticity leads to network-wide delay reorganization
• Circulant symmetry enables analytical stability

Related Skills

• kuramoto-brain-network
• complex-valued-kuramoto-control
• kuramoto-control-theory
• spiking-oscillation-mapping
• adaptive-bistable-qubit-control

Source

arXiv:2606.21508 - "Adaptive conduction delays and phase locking in spiking Haken Lighthouse networks" Authors: Stephen Coombes, Rüdiger Thul, Stefan Ruschel, Rachel Nicks Published: 2026-06-19 Link: http://arxiv.org/abs/2606.21508v1