Turing pattern formation of catalytic reaction diffusion systems in engineering applications

2003 ◽  
Vol 11 (3) ◽  
pp. 321-329 ◽  
Author(s):  
Xin-She Yang
Author(s):  
Houye Liu ◽  
Weiming Wang

Amplitude equation may be used to study pattern formatio. In this chapter, we establish a new mechanical algorithm AE_Hopf for calculating the amplitude equation near Hopf bifurcation based on the method of normal form approach in Maple. The normal form approach needs a large number of variables and intricate calculations. As a result, deriving the amplitude equation from diffusion-reaction is a difficult task. Making use of our mechanical algorithm, we derived the amplitude equations from several biology and physics models. The results indicate that the algorithm is easy to apply and effective. This algorithm may be useful for learning the dynamics of pattern formation of reaction-diffusion systems in future studies.


Sign in / Sign up

Export Citation Format

Share Document