‘Biologically-Inspired Reaction-Diffusion Networks’: An Introduction

Filed under: Uncategorized — frm @ 12:59 pm

Welcome to my new academic blog, where I plan to record my thoughts, readings and progress on my PhD at the University of Paisley, the title of which is ‘Biologically-Inspired Reaction-Diffusion Networks’.

Depending on how technical an explanation seems called for, I’ve been telling people my PhD is on ‘computer brains’ or ‘neural modelling’, and/or telling them the official title, to see if it makes any sense to them at all. Loosely speaking, I am trying to gain some insight into how thoughts arise using models based on reaction-diffusion equations. I am based in the School of Computer Science, but my background is mainly in physics, and I expect to be drawing on many different branches of science in my work.

The project is closely related to something I was working on a couple of years ago with my mother, Dinah Murray, and her colleague Mike Lesser, at Autism and Computing – a model designed to illustrate and shed light on their conception of the mind as a system of interests competing for attention. This idea explains autism as a difference in attention-using strategy, labelled ‘monotropism’; where most people have a range of interests aroused at any particular moment, those on the autistic spectrum have a tendency to focus their attention very tightly on only one or two concerns at any particular time. Switching the focus of attention is often uncomfortable, and interactions with autistic people can be made much easier and more fruitful by engaging with their existing attention tunnel rather than trying to wrench it onto another subject.

The mathematical model of the ‘interest system’ treats it as a reaction-diffusion system, with interests feeding on one another and action exhausting interest. Different calibrations of the model show features of monotropic attention use or its converse, polytropism.

For reference, this was the description of the PhD project in the advertisement which caught my attention:

The reaction-diffusion systems, being capable of pattern formation, describe numerous natural phenomena. In particular, they are known to model selforganizing behaviour of living brains. Neural selforganization implementated as bistable reaction-diffusion medium bears several disadvantages. First, neurons are not integral part of reaction-diffusion medium but distinctive from it components. Second, this medium requires three-molecular or variable rate two-molecular reactions, which is, in fact, rare phenomenon in nature.

In this project, we are going to develop realistic, purely reaction-diffusion models of neural activity. Mechanisms of formation of neural activity patterns and their effect on brain’s information processing will be investigated.


  1. I’d like to know more about the mathematical model you’re using. I’m a PhD candidate in applied math. You can email me at andreajorush@gmail.com.

    Comment by AndreaJoRush — October 31, 2007 @ 5:33 am

  2. This is really interesting. I am reading Turing’s paper The Chemical Basis of Morphogenesis and had a similar idea while reading, however I struggle grasping the mathematics behind it. I am a computer programmer learning this stuff by myself and I must confess this is not easy. I have a basic understanding of calculus (limits, derivative, integral, Fourrier transforms.) What do you suggest I study in order to well understand reaction-diffusion principles?

    Comment by Nicolas B. — August 17, 2012 @ 8:31 pm

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