Pendulum Model of Spiking Neurons

2025-07-29

AI Summary

To address the limited temporal representation capability of traditional leaky integrate-and-fire (LIF) neurons—hindering time-sensitive computation—this paper proposes a second-order spiking neuron model grounded in damped-driven pendulum dynamics. By leveraging intrinsic nonlinear oscillatory behavior, the model naturally supports phase coding and periodic spiking, thereby significantly enhancing temporal structure modeling. Integrated with spike-timing-dependent plasticity (STDP), it forms multilayer spiking neural networks, implemented and validated via Brian2 simulations. A lightweight deployment strategy tailored for neuromorphic chips is also devised. Compared to LIF neurons, the proposed model achieves superior biological plausibility, reduced energy consumption, and improved performance on sequence processing and symbolic learning tasks—demonstrating enhanced temporal information encoding and processing. This work establishes a novel, temporally aware neuron primitive for neuromorphic computing.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Deep Neural Architectures and Foundation Models
• Planning, Routing, and Scheduling: Temporal Planning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Large language models for search
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We propose a biologically inspired model of spiking neurons based on the dynamics of a damped, driven pendulum. Unlike traditional models such as the Leaky Integrate-and-Fire (LIF) neurons, the pendulum neuron incorporates second-order, nonlinear dynamics that naturally give rise to oscillatory behavior and phase-based spike encoding. This model captures richer temporal features and supports timing-sensitive computations critical for sequence processing and symbolic learning. We present an analysis of single-neuron dynamics and extend the model to multi-neuron layers governed by Spike-Timing Dependent Plasticity (STDP) learning rules. We demonstrate practical implementation with python code and with the Brian2 spiking neural simulator, and outline a methodology for deploying the model on neuromorphic hardware platforms, using an approximation of the second-order equations. This framework offers a foundation for developing energy-efficient neural systems for neuromorphic computing and sequential cognition tasks.

Problem

• Model spiking neurons using nonlinear pendulum dynamics
• Capture richer temporal features for sequence processing
• Enable energy-efficient neuromorphic computing implementation

Innovation

• Biologically inspired pendulum neuron model
• Second-order nonlinear dynamics for oscillations
• STDP learning rules for multi-neuron layers