期刊
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
卷 482, 期 -, 页码 597-610出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physa.2017.04.053
关键词
Hopf bifurcation; Turing instability; Pattern; Activator-inhibitor model
资金
- National Science Foundation of China [11571016, 61403115]
- Specialized Research Fund for Doctoral Program of Higher Education of China [20093401120001]
Gierer-Meinhardt system is one of prototypical pattern formation models. Turing instability could induce various patterns in this system. Hopf bifurcation analysis and its direction are performed on such diffusive model in this paper, by employing normal form and center manifold reduction. The effects of diffusion on the stability of equilibrium point and the bifurcated limit cycle from Hopf bifurcation are investigated. It is found that under some conditions, diffusion-driven instability, i.e, Turing instability, about the equilibrium point and the bifurcated limit cycle will happen, which are stable without diffusion. Those diffusion-driven instabilities will lead to the occurrence of spatially nonhomogeneous solutions. As a result, some patterns, like stripe and spike solutions, will form. The explicit criteria about the stability and instability of the equilibrium point and the limit cycle in the system are derived, which could be readily applied. Further, numerical simulations are presented to illustrate theoretical analysis. (C) 2017 Elsevier B.V. All rights reserved.
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