3 papers on complex modes of synchronization

[Thomas Wennekers]

Dear connectionists,

The following three papers on complex modes of synchronization
in networks of graded response and spiking neurons are now
available from the web page:

http://www.informatik.uni-ulm.de/ni/mitarbeiter/TWennekers.html

Regards, Thomas.


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Generalized and Partial Synchronization of Coupled Neural Networks

Frank Pasemann and Thomas Wennekers

to appear in "Network: Computation in Neural Systems"

Abstract:
Synchronization of neural signals has been proposed as a
temporal coding scheme representing cooperated computation
in distributed cortical networks. Previous theoretical
studies in that direction mainly focused on the
synchronization of coupled oscillatory subsystems and
neglected more complex dynamical modes, that already exist
on the single-unit level. In the present work we study the
parametrized time-discrete dynamics of two coupled recurrent
networks of graded neurons. Conditions for the existence
of partially synchronized dynamics of these systems are
derived, referring to a situation where only subsets of
neurons in each sub-network are synchronous. The coupled
networks can have different architectures and even a
different number of neurons. Periodic as well as
quasiperiodic and chaotic attractors constrained to a
manifold $M$ of synchronized components are observed.
Examples are discussed for coupled 3-neuron networks
having different architectures, and for coupled 2-neuron
and 3-neuron networks. Partial synchronization of different
degrees is demonstrated by numerical results for selected
sets of parameters. In conclusion, the results show that
synchronization phenomena far beyond completely synchronized
oscillations can occur even in simple coupled networks. The
type of the synchronization depends in an intricate way on   
stimuli, history and connectivity as well as other parameters
of the network. Specific inputs can further switch between
different operational modes in a complex way, suggesting a
similarly rich spatio-temporal behavior in real neural systems.

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Complete Synchronization in Coupled Neuromodules of Different Types

Frank Pasemann and Thomas Wennekers

Theory in Biosciences 118:267-283, 1999.

Abstract:
We discuss the parametrized dynamics of two coupled recurrent
neural networks comprising either additive sigmoid neurons in
discrete time or biologically more plausible time-continuous
leaky-integrate-and-fire cells. General conditions for the
existence of synchronized activity in such networks are given, 
which guarantee that corresponding neurons in both coupled
sub-networks evolve synchronously. It is, in particular,
demonstrated that even the coupling of totally different
network structures can result in complex dynamics constrained
to a synchronization manifold $M$. For additive sigmoid neurons
the synchronized dynamics can be periodic, quasiperiodic as
well as chaotic, and its stability can be determined by
Lyapunov exponent techniques. For leaky-integrate-and-fire
cells synchronized orbits are typically periodic, often with
an extremely long period duration. In addition to synchronized
attractors there often co-exist asynchronous periodic,
quasiperiodic and even chaotic attractors.

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"Generalized Types of Synchronization in Networks of
  Spiking Neurons"
 
  Thomas Wennekers and Frank Pasemann:

Submitted to Computational Neuroscience Conference, CNS 2000.
 
Abstract: 
The synchronization of neural signals has been proposed
as a temporal coding scheme in distributed cortical networks.
Theoretical studies in that direction mainly focused on the
synchronization of coupled oscillatory subsystems.
In the present work we show that several complex types
of synchronization previously described for graded response
neurons appear similarly also in biologically realistic
networks of spiking and compartmental neurons. This includes
synchronized complex spatio-temporal behavior, partial and
generalized synchronization.
The results suggest a similarly rich spatio-temporal behavior
in real neural systems and may guide experimental research
towards the study of complex modes of synchronization and
their neuromodulation.

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Thomas Wennekers
Max-Planck-Institute for Mathematics in the Sciences
Inselstrasse 22-26
04103 Leipzig
Germany

Phone: +49-341-9959-533
Fax:   +49-341-9959-555

Email: Thomas.Wennekers at mis.mpg.de

WWW : www.mis.mpg.de
      www.informatik.uni-ulm.de/ni/mitarbeiter/TWennekers.html
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