InterJournal Complex Systems, 205
Status: Submitted
Manuscript Number: [205]
Submission Date: 980831
Comment on manuscript revision number 53290
Ordering chaos in a neural network with linear feedback
Author(s): Michael Doebeli

Subject(s): CX.66

Category: Brief Article


This is an interesting note reporting how one can control chaos in a system of neurons that are connected by both first and second order Hebbian synapses. The control mechanism is very simple and works by assuming that every neuron feeds back linearly on itself. The strength of this feedback is the control parameter: the stronger the feedback, the simpler the resulting neural dynamics. Even though this ms was explicitly submitted as a brief article, I find the description of the results too short. More specifically: 1. The dynamics of the system are described in terms of the statistical average overlap m(t). If I understood correctly, this is the overlap with a given stored random pattern. If the dynamics of m(t) are simple, i.e. periodic, this means that the overlap with the stored pattern changes periodically over time. The control mechanism does not depend on the stored pattern to which the overlap m(t) refers. As a consequence, Figure 6 is not clear to me. This figure says that with negative control feedback, the overlap equilibrates at -1, i.e. at the negative fixpoint. Since the control mechanism does not depend on the pattern with which the overlap is measured, this result should hold for the overlap with any arbitrary pattern. This in turn does not seem to be possible. 2. It would be good to have some information about how robust the results are in terms of the parameters in the system. What is described in Figs. 2-6 is one single case in which the control worked. How general are these pictures? What are the crucial assumptions in the model for the control mechanism to work? For example, does the control also work when there are no second order synapses in the system? 3. There is not enough information given to reproduce the figures. 4. On l.12, second column of p. 3 it should read m(t=0) = 0.3 (not 0.2). In sum, this is an interesting note, but the author should provide some more information.

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