کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1898512 1044723 2013 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
State transition graph and stability of singular equilibria for piecewise linear biological models
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
State transition graph and stability of singular equilibria for piecewise linear biological models
چکیده انگلیسی

Many biological networks such as gene regulatory networks and neural networks can be modeled by piecewise linear switching systems of differential equations. For these biological network models, it is very difficult to describe the dynamics of the governing system near singular equilibria as they belong to the discontinuity set of the system. In this paper, using the concept of Filippov solutions, with the help of the state transition graph, and employing a generalized Lyapunov method, we establish some stability results for singular equilibria of a class of piecewise linear biological models. Our results generalize many existing ones. In particular, we present an affirmative answer to Conjecture 5.4 proposed in [R. Casey, H. de Jong, J.-L. Gouzé, Piecewise-linear models of genetic regulatory networks: Equilibria and their stability, Journal of Mathematical Biology 52 (1) (2006) 27–56].


► Provide an affirmative answer to a conjecture proposed by Casey, de Jong and Gouzé in 2006.
► Successfully apply a generalized Lyapunov method to a piecewise-linear network model.
► Introduce a new map that can be conveniently used in a state transition graph.
► Exponential stability is established.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica D: Nonlinear Phenomena - Volume 246, Issue 1, 1 March 2013, Pages 39–49
نویسندگان
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