کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4610675 1338578 2013 23 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Attractivity, multistability, and bifurcation in delayed Hopfieldʼs model with non-monotonic feedback
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Attractivity, multistability, and bifurcation in delayed Hopfieldʼs model with non-monotonic feedback
چکیده انگلیسی

For a system of delayed neural networks of Hopfield type, we deal with the study of global attractivity, multistability, and bifurcations. In general, we do not assume monotonicity conditions in the activation functions. For some architectures of the network and for some families of activation functions, we get optimal results on global attractivity. Our approach relies on a link between a system of functional differential equations and a finite-dimensional discrete dynamical system. For it, we introduce the notion of strong attractor for a discrete dynamical system, which is more restrictive than the usual concept of attractor when the dimension of the system is higher than one. Our principal result shows that a strong attractor of a discrete map gives a globally attractive equilibrium of a corresponding system of delay differential equations. Our abstract setting is not limited to applications in systems of neural networks; we illustrate its use in an equation with distributed delay motivated by biological models. We also obtain some results for neural systems with variable coefficients.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 255, Issue 11, 1 December 2013, Pages 4244–4266
نویسندگان
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