کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
7222321 1470398 2016 32 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Spatial resonance and Turing-Hopf bifurcations in the Gierer-Meinhardt model
ترجمه فارسی عنوان
رزونانس فضایی و دوچرخهای تورینگ-هوف در مدل گیرر-مینهارت
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
چکیده انگلیسی
Gierer-Meinhardt system as a molecularly plausible model has been proposed to formalize the observation for pattern formation. In this paper, the Gierer-Meinhardt model without the saturating term is considered. By the linear stability analysis, we not only give out the conditions ensuring the stability and Turing instability of the positive equilibrium but also find the parameter values where possible Turing-Hopf and spatial resonance bifurcation can occur. Then we develop the general algorithm for the calculations of normal form associated with codimension-2 spatial resonance bifurcation to better understand the dynamics neighboring of the bifurcating point. The spatial resonance bifurcation reveals the interaction of two steady state solutions with different modes. Numerical simulations are employed to illustrate the theoretical results for both the Turing-Hopf bifurcation and spatial resonance bifurcation. Some expected solutions including stable spatially inhomogeneous periodic solutions and coexisting stable spatially steady state solutions evolve from Turing-Hopf bifurcation and spatial resonance bifurcation respectively.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Real World Applications - Volume 31, October 2016, Pages 356-387
نویسندگان
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