کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5774625 | 1413563 | 2017 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Exponential number of stationary solutions for Nagumo equations on graphs
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We study the Nagumo reaction-diffusion equation on graphs and its dependence on the underlying graph structure and reaction-diffusion parameters. We provide necessary and sufficient conditions for the existence and nonexistence of spatially heterogeneous stationary solutions. Furthermore, we observe that for sufficiently strong reactions (or sufficiently weak diffusion) there are 3n stationary solutions out of which 2n are asymptotically stable. Our analysis reveals interesting relationship between the analytic properties (diffusion and reaction parameters) and various graph characteristics (degree distribution, graph diameter, eigenvalues). We illustrate our results by a detailed analysis of the Nagumo equation on a simple graph and conclude with a list of open questions.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 455, Issue 2, 15 November 2017, Pages 1749-1764
Journal: Journal of Mathematical Analysis and Applications - Volume 455, Issue 2, 15 November 2017, Pages 1749-1764
نویسندگان
Petr StehlÃk,