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4
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0003776898
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it Synaptic Transmission, in, edited by, E. R Kandel, J. H. Schwartz, T. M. Jessell, Elsevier, New York
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(1991)
Principles of Neuroscience
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Kandel, E.R.1
Siegelbaum, S. A2
Schwartz, J.H.3
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84927465857
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While we were completing this paper, we received an article by Okuda [, ]. In this work the author claims that in order to have n cluster states in a network of phase oscillators, it is indispensable to have a mode of order n in the Fourier expansion of the phase interaction. The argument of the author seems to us doubtful since it is based on a linear stability analysis in cases where marginality occurs. Moreover, in our model we are able to find stable three cluster states for suitable initial conditions although the interaction contains only modes 1 and 2.
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(1993)
Physica D
, vol.63
, pp. 424
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16
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84927460073
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The observation that the system oscillates between the two alternative two cluster states and spends more and more time near each one may seem in contradiction with the fact that the histogram of Δ (Sec. III,A) is monomodal. This histogram was obtained starting from random initial conditions. In order to solve this apparent paradox, we suggest that the basin of attraction of one of the two cluster states is actually much bigger than the basin of attraction of the other. As a consequence the network enters into the oscillatory regime nearer to one of the cluster states. Then, the system performs oscillations and eventually converges due to the finite precision of the computer. The number of these oscillations depends barely on the initial conditions, since it varies only logarithmically with the deviation from the two cluster states at the beginning of these oscillations. Therefore the system is expected to end almost always in the same final state.
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84927465857
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Okuda describes in a footnote of his paper [, ] a phenomenon that seems similar to the one we have described in Part 3. He also suggests an interpretation in terms of heteroclinicity. This provides some indication of the generality of our results.
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(1993)
Physica D
, vol.63
, pp. 424
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