Latest News

About CAMQ

Information for Authors

Editorial Board

Browse CAMQ Online

Subscription and Pricing

CAMQ Contacts

CAMQ Home

 

Volume 20,     Number 2,     Summer 2012

 

TURING INSTABILITY GENERATED FROM
DISCRETE DIFFUSION-MIGRATION SYSTEMS
LU ZHANG, GUANG ZHANG AND WENYING FENG

Abstract. In this paper, Turing instability for a class of discrete diffusion-migration dynamical systems is studied. Different from the corresponding continuous model, it is shown that the discrete system can generate Turing instability and therefore produce Turing patterns. Our approach is by the commonly applied linear stability analysis for nonlinear evolution equations as well as the methodologies of discretizing the analogous differential equations to obtain discrete approximation. To compare different discrete forms generated from the same continuous system, we develop three discrete models for the Lotka-Volterra competitive diffusion-migration driven system by applying the Euler, exponential and fractional discretizing methods and prove instability conditions for each of them respectively. Our simulation results show the substantial differences among the patterns obtained from the three different discrete forms. In addition, we also investigate evaluation of the Turing patterns by varying the instability parameters.

 

Download PDF Files
 
(Subscribers Only)

© 2006-2012 Canadian Applied Mathematics Quarterly (CAMQ)