soliton-waves-wstdp-snn

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

1. Self-organizing propagation: Network learns to sustain propagation in one direction while suppressing reverse propagation
2. Phase encoding: Boundary position between competing waves encodes relative phase and frequency of sources
3. 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