Commun. Comput. Phys.,
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Volume 3.

Numerical Investigations of the Dynamical Behaviors and Instabilities for the Gierer-Meinhardt System

Zhonghua Qiao 1*

1 Center for Research in Scientific Computation, North Carolina State University, Raleigh, North Carolina, 27695-8205, USA.

Received 7 January 2007; Accepted (in revised version) 28 May 2007
Available online 9 October 2007


This work is concerned with the numerical simulations on the Gierer-Meinhardt activator-inhibitor models. We consider the case when the inhibitor time constant $\tau$ is non-zero. In this case, oscillations and pulse splitting are observed numerically. Numerical experiments are carried out to investigate the dynamical behaviors and instabilities of the spike patterns. The numerical schemes used are based upon an efficient moving mesh finite element method which distributes more grid points near the localized spike regions.

AMS subject classifications: 65M50, 65M60

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Key words: Gierer-Meinhardt model, moving finite element method, pulse splitting, spikes.

*Corresponding author.
Email: (Z.-H. Qiao)

The Global Science Journal