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|Title:||On the Gierer-Meinhardt system with precursors|
|Keywords:||Pattern formation;Mathematical biology;Singular perturbation;Precursor|
|Publisher:||American Institute of Mathematical Sciences|
|Citation:||Discrete and Continuous Dynamical Systems (DCDS-A), 25(1): 363-398|
|Abstract:||We consider the Gierer-Meinhardt system with a for the activator. Such an equation exhibits a typical Turing bifurcation of the second kind, i.e., homogeneous uniform steady states do not exist in the system. We establish the existence and stability of N-peaked steady-states in terms of the precursor and the inhibitor diffusivity. It is shown that the precursor plays an essential role for both existence and stability of spiky patterns. In particular, we show that precursors can give rise to instability. This is a new effect which is not present in the homogeneous case.|
|Appears in Collections:||Dept of Mathematics Research Papers|
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