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Analysis of Turing Instability for Biological Models

  • Daiana Rodrigues
  • Luis Paulo Barra
  • Marcelo Lobosco
  • Flávia Bastos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8584)

Abstract

Reaction-diffusion equations are often used to model biological phenomena. This type of system can produce stable spatial patterns from an uniform initial distribution. This phenomenon is known as Turing instability. This paper presents an analysis of the Turing instability for three biological models: a) Schnakenberg model, b) glycolysis model and c) blood coagulation model. The method of lines is used in the numerical solution, and the spatial discretization is done using a finite difference scheme. The resulting system of ordinary differential equations is then solved by an adaptive integration scheme with the use of SciPy, a Python package for scientific computing.

Keywords

Turing instability Reaction-Diffusion Equations Schnakenberg model glycolysis model blood coagulation model 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Daiana Rodrigues
    • 1
  • Luis Paulo Barra
    • 1
  • Marcelo Lobosco
    • 1
  • Flávia Bastos
    • 1
  1. 1.Graduate Program in Computational ModellingFederal University of Juiz de ForaJuiz de ForaBrazil

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