Numerical Investigations of the Dynamical Behaviors and Instabilities for the Gierer-Meinhardt System (Communications in Computational Physics, 2018)
This work is concerned with the numerical simulations on the Gierer-Meinhardt activator-inhibitor models. We consider the case when the inhibitor timeconstant τ is non-zero. In this case, oscillations and pulse splitting are observed numerically. Numerical experiments are carried out to investigate the dynamical behaviorsand instabilities of the spike patterns. The numerical schemes used are based upon anefficient moving mesh finite element method which distributes more grid points nearthe localized spike regions.