On the sensitive dependence on initial conditions of the dynamics of networks of spiking neurons |
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Authors: | Arunava Banerjee |
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Institution: | (1) Computer and Information Science and Engineering Department, University of Florida, Gainesville, FL, 32611-6120 |
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Abstract: | We have previously formulated an abstract dynamical system for networks of spiking neurons and derived a formal result that
identifies the criterion for its dynamics, without inputs, to be “sensitive to initial conditions”. Since formal results are
applicable only to the extent to which their assumptions are valid, we begin this article by demonstrating that the assumptions
are indeed reasonable for a wide range of networks, particularly those that lack overarching structure. A notable aspect of
the criterion is the finding that sensitivity does not necessarily arise from randomness of connectivity or of connection
strengths, in networks. The criterion guides us to cases that decouple these aspects: we present two instructive examples
of networks, one with random connectivity and connection strengths, yet whose dynamics is insensitive, and another with structured
connectivity and connection strengths, yet whose dynamics is sensitive. We then argue based on the criterion and the gross
electrophysiology of the cortex that the dynamics of cortical networks ought to be almost surely sensitive under conditions
typically found there. We supplement this with two examples of networks modeling cortical columns with widely differing qualitative
dynamics, yet with both exhibiting sensitive dependence. Next, we use the criterion to construct a network that undergoes
bifurcation from sensitive dynamics to insensitive dynamics when the value of a control parameter is varied. Finally, we extend
the formal result to networks driven by stationary input spike trains, deriving a superior criterion than previously reported.
Action Editor: John Rinzel |
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Keywords: | Dynamical systems Sensitive dependence Spiking neurons |
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