کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4625217 | 1340329 | 2008 | 16 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Graphic requirements for multistability and attractive cycles in a Boolean dynamical framework
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
To each Boolean function and each x∈n{0,1}, we associate a signed directed graph G(x), and we show that the existence of a positive circuit in G(x) for some x is a necessary condition for the existence of several fixed points in the dynamics (the sign of a circuit being defined as the product of the signs of its edges), and that the existence of a negative circuit is a necessary condition for the existence of an attractive cycle. These two results are inspired by rules for discrete models of genetic regulatory networks proposed by the biologist R. Thomas. The proof of the first result is modelled after a recent proof of the discrete Jacobian conjecture.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Applied Mathematics - Volume 41, Issue 3, September 2008, Pages 335-350
Journal: Advances in Applied Mathematics - Volume 41, Issue 3, September 2008, Pages 335-350