| name | soliton-waves-wstdp-snn |
| description | Soliton-like wave propagation in recurrent spiking neural networks with weighted STDP. Use when studying cortical traveling waves, activity zone delimitation, spatial memory formation, or self-propagating neural activity patterns. |
| tags | ["spiking-neural-networks","STDP","cortical-waves","soliton","recurrent-networks"] |
Soliton-like Waves in Two-Dimensional Recurrent Spiking Neural Networks with Weighted STDP
arXiv: 2606.21432v1 (June 19, 2026)
Authors: Ch. Meessen
Categories: cs.NE, q-bio.NC
Core Contribution
Demonstrates that recurrent spiking neural networks with weighted STDP spontaneously generate stable, self-propagating wave packets (dissipative solitons) that maintain spatial profiles, propagate at constant speed, and annihilate upon collision.
Key Methodology
1. Minimal Biologically Plausible Neuron Model
Discrete-time spiking neuron combining:
- Multiplicative STDP (WSTDP): Weight-dependent spike-timing-dependent plasticity
- Divisive normalization: Biologically plausible dendritic implementation using only local information
- Homeostatic threshold adaptation: Maintains stability
- One-step refractory period: Prevents immediate re-firing
2. Network Architecture
- Excitatory-inhibitory neuron pairs in 2D recurrent network
- Periodic localized stimulation
- Geometric asymmetry: inhibitory radius > excitatory radius
- Initial inhibitory synapses stronger than excitatory
3. Emergent Phenomena
- Soliton formation: Self-propagating wave packets with stable spatial profiles
- Constant velocity propagation: Waves travel at fixed speed
- Collision annihilation: Frontal collisions destroy waves
- Direction learning: WSTDP engraves propagation direction into synaptic weights
- Boundary formation: Simultaneous sources create semi-persistent boundaries encoding relative phase/frequency
Key Findings
- Self-organizing propagation: Network learns to sustain propagation in one direction while suppressing reverse propagation
- Phase encoding: Boundary position between competing waves encodes relative phase and frequency of sources
- Local computation only: Dendritic implementation requires only locally available information at each binary junction
Implications
Provides minimal computational framework for studying:
- Cortical traveling waves
- Activity zone delimitation
- Spatial memory formation from local plasticity rules
Activation Keywords
soliton waves, STDP, traveling waves, cortical dynamics, recurrent SNN, self-propagating activity, collision annihilation, spatial memory, divisive normalization
Related Work
- Dissipative solitons in physics
- Cortical traveling waves in visual cortex
- STDP-based learning rules
- Recurrent neural network dynamics
