C. Marcus, F. Waugh, and R. Westervelt, "Nonlinear dynamics and stability of analog neural networks, " Physica D, vol. 51, p. 1991, 1991. (special issue). Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Recurrent Neural Networks for Adaptive Temporal Processing - Bengio, Frasconi, Gori (1993) (2 citations) (Correct)
....the map M is hyperbolic for the map M l . For a recurrent net, the kind of attractor depends on the weight matrix. In particular, for a network defined by a t = W tanh(a t Gamma1 ) u t , if W is symmetric and its minimum eigenvalue is greater than 1, then the attractors are all fixed points [46]. On the other hand, if jW j 1 or if the system is linear and stable, the system has a single fixed point attractor at the origin. Definition 3 The basin of attraction of an attractor X is the set fi(X) of points a converging to X under the map M , i.e. fi(X) fa : 8ffl; 9l; 9x 2 X s:t: kM l ....
C. Marcus, F. Waugh, and R. Westervelt, "Nonlinear dynamics and stability of analog neural networks, " Physica D, vol. 51, p. 1991, 1991. (special issue).
Frustrated Chaos in Biological Networks - Bersini, Calenbuhr (Correct)
....by opening here and there the connectivity matrix. One great weakness remains in this analysis of frustration in HN: The impossibility (in 15 contrast with the classical characterisation of frustration in (Toulouse, 1997; Hiernaux, 1977; Amit, 1989; Sherrington, 1990; Marcus and Westervelt, 1987; Marcus et al. 1991; Bersini and Calenbuhr, 1995; Daido, 1992; Omata and Yamaguchi, 1988; Thomas, 1991) to anticipate the appearance of chaos due to a certain connectivity pattern and accordingly to clearly identify what is responsible in the matrix for this further source of instability (besides the presence of odd ....
Marcus, C.M., F.R. Waugh and R.M. Westervelt. (1991). Nonlinear dynamics and stability of analog neural networks - in Physica D 51 - pp. 234-247.
Qualitative Analysis of a Neural Network Model with.. - Campbell, Ruan, Wei (Correct)
....delays in response or transmission have a dramatic influence on the dynamics of the neural network models. In particular, a time delay can induce sustained oscillations in convergent networks (see Marcus and Westervelt [17] and even chaos in threeneuron networks (see Marcus, Waugh and Westervelt [16]) Recently, research has focused on the dynamics of neural networks with multiple delays (see Babcock and Westervelt [1] Baldi and Atiya [2] Campbell [5] Majee and Roy [14] Olien and B elair [18] Wei and Ruan [21] and many interesting dynamical phenomena have been observed. In this paper, ....
C. M. Marcus, F. R. Waugh and R. M. Westervelt, Nonlinear dynamics and stability of analog neural networks, Physica D 51 (1991), 234--247.
Analysis of Dynamical Systems using Predicate Transformers.. - Sintzoff, Geurts (1995) (3 citations) (Correct)
....Blum and Wang [34] study neural networks and their dynamics by considering small systems which are more understandable and by composing these. They focus their attention on bifurcation properties, and on oscillations produced by small systems and composed ones. Marcus, Waugh and Westervelt [35] adopt a global viewpoint for extracting analytic results about fixed points, stability, and convergence of different neural networks. Why do we present those works Because we also consider small systems composed into more complex ones and we try to study the behaviour of these complex systems ....
Marcus, C.M., Waugh, F.R., and Westervelt, R.M. Nonlinear dynamics and stability of analog neural networks. Physica D, 51:234--247, 1992. This article was processed using the L a T E X macro package with LLNCS style
Learning Long-Term Dependencies with Gradient Descent is.. - Bengio, Simard, Frasconi (1994) (105 citations) (Correct)
....the map M is hyperbolic for the map M l . For a recurrent net, the kind of attractor depends on the weight matrix. In particular, for a network defined by a t = W tanh(a t Gamma1 ) u t , if W is symmetric and its minimum eigenvalue is greater than 1, then the attractors are all fixed points [17]. On the other hand, if jW j 1 or if the system is linear and stable, the system has a single fixed point attractor at the origin. Definition 3 The basin of attraction of an attractor X is the set fi(X) of points a converging to X under the map M , i.e. fi(X) fa : 8ffl; 9l; 9x 2 X s:t: kM ....
C.M. Marcus, F.R. Waugh, and R.M. Westervelt, "Nonlinear Dynamics and Stability of Analog Neural Networks", Physica D 51 (special issue), 1991, pp. 234-247.
Recurrent Neural Networks for Adaptive Temporal Processing - Bengio, Frasconi, Gori, Soda (1993) (2 citations) (Correct)
....the map M is hyperbolic for the map M l . For a recurrent net, the kind of attractor depends on the weight matrix. In particular, for a network defined by a t = W tanh(a t Gamma1 ) u t , if W is symmetric and its minimum eigenvalue is greater than 1, then the attractors are all fixed points [48]. On the other hand, if jW j 1 or if the system is linear and stable, the system has a single fixed point attractor at the origin. Definition 3 The basin of attraction of an attractor X is the set fi(X) of points a converging to X under the map M , i.e. fi(X) fa : 8ffl; 9l; 9x 2 X s:t: kM ....
C. Marcus, F. Waugh, and R. Westervelt, "Nonlinear dynamics and stability of analog neural networks," Physica D, vol. 51, p. 1991, 1991. (special issue).
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