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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
89/2002

Total and partial amplitude death in networks of diffusively coupled oscillators

Fatihcan M. Atay

Abstract

Networks of weakly nonlinear oscillators are considered with diffusive and time-delayed coupling. Averaging theory is used to determine parameter ranges for which the network experiences amplitude death, whereby oscillations are quenched and the equilibrium solution has a large domain of attraction. The amplitude death is shown to be a common phenomenon, which can be observed regardless of the precise nature of the nonlinearities and under very general coupling conditions. In addition, when the network consists of dissimilar oscillators, there exist parameter values for which only parts of the network are suppressed. Sufficient conditions are derived for total and partial amplitude death in arbitrary network topologies with general nonlinearities, coupling coefficients, and connection delays.

Received:
30.09.02
Published:
30.09.02
MSC Codes:
34C15, 34K, 92B20
PACS:
02.30.Ks, 84.35.+i, 87.10.+e, 05.45.+b
Keywords:
coupled oscillators, time delay, stability, neural networks

Related publications

inJournal
2003 Repository Open Access
Fatihcan M. Atay

Total and partial amplitude death in networks of diffusively coupled oscillators

In: Physica / D, 183 (2003) 1/2, pp. 1-18