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
44/1998

Synchronized chaos and other coherent states for two coupled neurons

Frank Pasemann

Abstract

The parametrized time-discrete dynamics of two recurrently coupled chaotic neurons is investigated. Basic dynamical features of this system are demonstrated for symmetric couplings of identical neurons. Periodic as well as chaotic orbits constrained to a manifold M of synchronized states are observed. Parameter domains for locally stable synchronization manifolds M are determined by numerical simulations. In addition to the synchronized dynamics there often co-exist periodic, quasiperiodic and even chaotic attractors representing different kinds of non-synchronous coherent dynamics. Simulation results for selected sets of parameters are presented, and synchronization conditions for systems with non-identical neurons are derived. Also these more general systems inherit the above mentioned dynamical properties.

Received:
Oct 21, 1998
Published:
Oct 21, 1998

Related publications

inJournal
1999 Repository Open Access
Frank Pasemann

Synchronized chaos and other coherent states for two coupled neurons

In: Physica / D, 128 (1999) 2-4, pp. 236-249