Attractor and saddle node dynamics in heterogeneous neural fields
نویسندگان
چکیده
Background Neural field models, such as [1,2] are continuum limits of large-scale neural networks. Typically, their dynamic variables describe either mean voltage [2] or mean firing rate [1,3] of a population element of neural tissue (see [4,5] for recent reviews). The present article considers the paradigmatic Amari equation [2] describing the spatiotemporal dynamics of mean potential V (x, t) over a cortical d-dimensional manifold ⊂ Rd:
منابع مشابه
بهبود بازشناسی مقاوم الگو در شبکه های عصبی بازگشتی جاذب از طریق به کارگیری دینامیک های آشوب گونه
In this paper, two kinds of chaotic neural networks are proposed to evaluate the efficiency of chaotic dynamics in robust pattern recognition. The First model is designed based on natural selection theory. In this model, attractor recurrent neural network, intelligently, guides the evaluation of chaotic nodes in order to obtain the best solution. In the second model, a different structure of ch...
متن کاملIntermittency and Jakobson’s theorem near saddle-node bifurcations
We discuss one parameter families of unimodal maps, with negative Schwarzian derivative, unfolding a saddle-node bifurcation. We show that there is a parameter set of positive but not full Lebesgue density at the bifurcation, for which the maps exhibit absolutely continuous invariant measures which are supported on the largest possible interval. We prove that these measures converge weakly to a...
متن کاملJakobson’s Theorem near saddle-node bifurcations
We discuss one parameter families of unimodal maps, with negative Schwarzian derivative, unfolding a saddle-node bifurcation. It was previously shown that for a parameter set of positive Lebesgue density at the bifurcation, the maps possess attracting periodic orbits of high period. We show that there is also a parameter set of positive density at the bifurcation, for which the maps exhibit abs...
متن کاملTwo-parameter Locus of Boundary Crisis: Mind the Gaps!
Boundary crisis is a mechanism for destroying a chaotic attractor when one parameter is varied. In a two-parameter setting the locus of boundary crisis is associated with curves of homoor heteroclinic tangency bifurcations of saddle periodic orbits. It is known that the locus of boundary crisis contains many gaps, corresponding to channels (regions of positive measure) where a non-chaotic attra...
متن کاملDelay-induced Multistability in a Generic Model for Excitable Dynamics
Motivated by real-world excitable systems such as neuron models and lasers, we consider a paradigmatic model for excitability with a global bifurcation, namely a saddle-node bifurcation on a limit cycle. We study the effect of a time-delayed feedback force in the form of the difference between a system variable at a certain time and at a delayed time. In the absence of delay the only attractor ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014