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Classifying and quantifying basins of attraction
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2015A scheme is proposed to classify the basins for attractors of dynamical systems in arbitrary dimensions. There are four basic classes depending on their size and extent, and each class can be further quantified to facilitate comparisons. The calculation uses a Monte Carlo method and is applied to numerous common dissipative chaotic maps and flows in ...
J. C. Sprott, Anda Xiong
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Basins of Attraction in Experimental Nonlinear Oscillators
International Journal of Bifurcation and Chaos, 1998This paper addresses two relatively simple but fundamental questions in nonlinear oscillations: Given an arbitrary initial condition where will the trajectory go, and how long will it take to get there? These related questions are addressed from an experimental perspective where generating global transient behavior has received relatively little ...
Virgin, L. N. +4 more
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Nondeterministic basin of attraction
Chaos, Solitons & Fractals, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Stochastic basins of attraction for metastable states
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2016Basin of attraction of a stable equilibrium point is an effective concept for stability analysis in deterministic systems; however, it does not contain information on the external perturbations that may affect it. Here we introduce the concept of stochastic basin of attraction (SBA) by incorporating a suitable probabilistic notion of basin.
Larissa Serdukova +3 more
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Basins of attraction in driven dynamical systems
Physical Review A, 1989The organization of multiple coexisting basins of attraction in two-dimensional driven dynamical systems is studied. This study is carried out, in particular, for the laser with modulated parameter and the H\'enon map. Basin organization is governed primarily by the ordering of heteroclinic and homoclinic connections of regular saddles.
, Eschenazi, , Solari, , Gilmore
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Attractors/Basin of Attraction
2020It is a controversial issue to decide who first coined the term “attractor”. According to Peter Tsatsanis, the editor of the English version of Predire n’est pas expliquer, it was Rene Thom who first introduced such a term. It is necessary, however, to remember that Thom thought that it was first introduced by the American mathematician Steven Smale ...
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Basins of attraction revisited
1990 IJCNN International Joint Conference on Neural Networks, 1990A new method is presented for displaying the basins of attraction of memory states of a neural network model. This method provides evidence that these basins of attraction remain mostly regular even as the number of stored states increases. Some effects of the location and number of stored states can be seen intuitively in the results of these graphs ...
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Attracting Basins of Certain Nonholomorphic Maps
International Journal of Bifurcation and Chaos, 1998Attractive basins of a function [Formula: see text] are considered. The function Fc(z) is obtained by a perturbation of a "two-dimensional tent map" [Formula: see text]. We prove that the immediate attractive basins of the function F4/3(z) consist of six triangular regions which are subdivisions of a equilateral triangle by three medians.
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Basin of attraction in networks of multistate neurons
Physical Review E, 1993The retrieval dynamics of an extremely diluted network of three-state neurons designed by the projection rule is investigated. Depending on the parameters of the model four different fixed points with different stability can exist. Only one of them corresponds to full retrieval. It is discussed how the parameters of the model must be chosen in order to
, Bouten, , Engel
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Synaptic depression enlarges basin of attraction
Neurocomputing, 2005Neurophysiological experiments show that synaptic depression controls a gain for presynaptic inputs. However, the functional roles of this gain control remain unknown. We propose that one of the functional roles is to enlarge basins of attraction. To verify this, we employ an associative memory model.
Matsumoto, N. +3 more
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