Pendulum Model of Spiking Neurons

TL;DR

This paper introduces a biologically inspired spiking neuron model based on damped, driven pendulum dynamics, capturing richer temporal features for sequence processing and neuromorphic applications.

Contribution

The paper presents a novel second-order nonlinear pendulum-based neuron model that enhances temporal encoding and supports phase-based spike timing, extending traditional neuron models.

Findings

Model captures oscillatory and phase-based spike encoding.

Supports sequence processing and symbolic learning.

Demonstrated implementation with Python and Brian2.

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.