Pattern dynamics of a Gierer-Meinhardt model with spatial effects

Interactions of activator and inhibitor can be widely applied in different fields. As a result, dynamical behaviors of an activator-inhibitor model with different sources are investigated. We obtained the condition of Turing bifurcation by using linear stability analysis, and the amplitude equation by employing multiple scale analysis. Moreover, the stability of amplitude equation was presented. It turned out that the model can show spot patterns, stripe patterns and the coexistence of spot and stripe patterns. Numerical simulations well validate our theoretical analysis. Our results highlight the relationship between pattern formation and variation of biological tissues.