On Modelling Pattern Formation by Activator-Inhibitor Systems.

Abstract

The formation of spatially patterned structures in biological organisms has been modelled in recent years by various mechanisms, including pairs of reaction-diffusion equations u sub t = D1 laplacian u + f(u,v), v sub t = D2 laplacian v + g(u,v). Their analysis has been by computer simulation. In some cases, u can be interpreted as an activator and v an inhibitor. The following problem is treated: given a pattern u = phi(x) v = psi(x), find a system which has it as a stable stationary solution (stability is used in various senses in the paper). This inverse problem is shown to have solutions for reasonable phi and psi. The solutions constructed are of activator-inhibitor type with D2 > D1. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1977
Accession Number
ADA038957

Entities

People

  • Paul C. Fife

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Boundaries
  • Chemical Kinetics
  • Computer Simulations
  • Computers
  • Contracts
  • Diffusion
  • Eigenvalues
  • Equations
  • Inhibition
  • Inhibitors
  • Inverse Problems
  • Kinetics
  • Mathematics
  • North Carolina
  • Simulations
  • Stationary
  • United States

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra
  • Vision Science/Vision Psychology/Cognitive Neuroscience.