International Journal of Advanced and Applied Sciences

Int. j. adv. appl. sci.

EISSN: 2313-3724

Print ISSN: 2313-626X

Volume 4, Issue 4  (April 2017), Pages:  22-26

Title: Pattern formation for a type of reaction diffusion system with cross diffusion

Author(s):  Shaker M. Rasheed *, Joseph G. Abdulahad, Viyan A. Mohammed Salih


Department of Mathematics, Faculty of Science, University of Zakho, Kurdistan Region, Iraq

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In this paper, pattern formation for a Schnakenberg model is studied in one and two dimensions. The model has been studied when the diffusion is nonlinear and so called cross diffusion. The conditions of diffusion driven instability are applied to this model and shown that this model can formulate patterns, and the existence of bifurcation for specific parameters are shown and for different values of wave number k. The use of COMSOL Multiphysics finite element package in simulation shows nice graphs of pattern formations in two dimensions. 

© 2017 The Authors. Published by IASE.

This is an open access article under the CC BY-NC-ND license (

Keywords: Schnakenberg model, Pattern formation, Cross diffusion

Article History: Received 5 December 2016, Received in revised form 10 February 2017, Accepted 18 February 2017

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Rasheed SM, Abdulahad JG, and Salih VAM (2017). Pattern formation for a type of reaction diffusion system with cross diffusion. International Journal of Advanced and Applied Sciences, 4(4): 22-26


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