Search

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
38/2001

Complex dynamics and the structure of small neural networks

Frank Pasemann

Abstract

The discrete-time dynamics of particular two and three neuron networks is studied with respect to non-trivial bifurcation scenarios. Interesting dynamical properties like periodic, quasi-periodic and chaotic attractors are observed, many of them coexisting for one and the same set of parameters. Symmetries in parameter space leading to equivalent dynamics are considered. Conditions on the connectivity of these small netwoks, involving excitation as well as inhibition, are derived which admit complex dynamics for these systems.

Received:
Jul 12, 2001
Published:
Jul 12, 2001

Related publications

inJournal
2002 Repository Open Access
Frank Pasemann

Complex dynamics and the structure of small neural networks

In: Network : computation in neural systems, 13 (2002) 2, pp. 195-216