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The Relevance of the Time Domain to Neural Network Models pp 9–32Cite as

Adaptation and Contraction Theory for the Synchronization of Complex Neural Networks

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Part of the book series: Springer Series in Cognitive and Neural Systems ((SSCNS,volume 3))

Abstract

In this chapter, we will present two different approaches to solve the problem of synchronizing networks of interacting dynamical systems. The former will be based on making the coupling between agents in the network adaptive and evolving so that synchronization can emerge asymptotically. The latter will be using recent results from contraction theory to give conditions on the node dynamics and the network topology that result into the desired synchronized motion. The theoretical results will be illustrated by means of some representative examples, including networks of neural oscillators.

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Notes

  1. 1.

    A function F:I→ℝ is positive definite if F(x)>0, ∀x∈I, x≠0 and F(0)=0. A function f:ℝ≥0→ℝ≥0 is of class k if it is continuous, positive definite and strictly increasing.

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Author information

Authors and Affiliations

  1. Department of Systems and Computer Engineering, University of Naples Federico II, Naples, Italy

    Pietro DeLellis, Mario di Bernardo & Giovanni Russo

  2. Department of Engineering Mathematics, University of Bristol, Bristol, UK

    Mario di Bernardo

Authors
  1. Pietro DeLellis
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  2. Mario di Bernardo
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  3. Giovanni Russo
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Corresponding author

Correspondence to Mario di Bernardo .

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Editors and Affiliations

  1. T.J. Watson Research Center, IBM Corporation, 1101 Kitchawan Road, Yorktown Heights, 10598, New York, USA

    A. Ravishankar Rao

  2. Research Center, Dept. Silicon Technology, IBM Thomas J. Watson, 1101 Kitchawan Road, Yorktown Heights, 10598, New York, USA

    Guillermo A. Cecchi

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DeLellis, P., di Bernardo, M., Russo, G. (2012). Adaptation and Contraction Theory for the Synchronization of Complex Neural Networks. In: Rao, A., Cecchi, G. (eds) The Relevance of the Time Domain to Neural Network Models. Springer Series in Cognitive and Neural Systems, vol 3. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-0724-9_2

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