Abstract
We explore the map \(x \mapsto (\alpha x + \gamma x^3)e^{-\beta x^2}\), which depending on the parameters displays a variety of different behaviours, both as a single map and when arranged in a coupled map lattice. The map can take on excitable and various oscillatory guises. For parameter values that result in excitable behaviour, we obtain a system that is roughly similar to a network of neurons that build up activation until they exceed the threshold and then fire some activation to their neighbours, depleting themselves in the process. We found that a higher communication rate and a lower threshold do not necessarily, and do not linearly result in a faster or more pervasive spread of activation. In fact, limits to communication can help the spread of activity.
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Loengarov, A., Tereshko, V. (2009). Activation Dynamics in Excitable Maps: Limits to Communication Can Facilitate the Spread of Activity. In: Alippi, C., Polycarpou, M., Panayiotou, C., Ellinas, G. (eds) Artificial Neural Networks – ICANN 2009. ICANN 2009. Lecture Notes in Computer Science, vol 5769. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04277-5_62
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DOI: https://doi.org/10.1007/978-3-642-04277-5_62
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04276-8
Online ISBN: 978-3-642-04277-5
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