Mode transitions in a model reaction-diffusion system driven by domain growth and noise
Related Experiment Video
Updated: Aug 7, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Iain Barrass1, Edmund J Crampin, Philip K Maini
1Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford, OX1 3LB, UK.
Abstract:
Pattern formation in many biological systems takes place during growth of the underlying domain. We study a specific example of a reaction-diffusion (Turing) model in which peak splitting, driven by domain growth, generates a sequence of patterns. We have previously shown that the pattern sequences which are presented when the domain growth rate is sufficiently rapid exhibit a mode-doubling phenomenon. Such pattern sequences afford reliable selection of certain final patterns, thus addressing the robustness problem inherent of the Turing mechanism. At slower domain growth rates this regular mode doubling breaks down in the presence of small perturbations to the dynamics. In this paper we examine the breaking down of the mode doubling sequence and consider the implications of this behaviour in increasing the range of reliably selectable final patterns.
More Related Videos
06:55Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
10:33A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates
Published on: February 23, 2018
Related Concept Videos
Modeling with Differential Equations
Reaction Mechanisms: The Steady-State Approximation
Entropy Change in Reversible Processes
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
Transient and Steady-state Response
These test signals are integral in designing control systems to exhibit two key performance aspects: transient response and steady-state response.
Theories of Dissolution: The Danckwerts' Model and Interfacial Barrier Model
Current Growth And Decay In RL Circuits