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Investigating mixed-sign equilibria for nonlinear collective decision-making systems
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-6367-6302
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0003-4142-6502
2017 (English)In: Proceedings from the 2017 IEEE 56th Annual Conference on Decision and Control (CDC), December 12-15, 2017, Melbourne, Australia, 2017, p. 781-786Conference paper, Published paper (Refereed)
Abstract [en]

In this paper we provide necessary conditions for the existence of multiple equilibrium points for a class of non-linear cooperative networked systems with saturating interactions which describe models of collective decision-making. The multiple steady states of the dynamics represent the possible outcomes of a decision process, and, except for one positive and one negative, have all mixed signs. The conditions we obtain can be formulated in terms of the algebraic connectivity of the network and are inspired by Perron-Frobenius arguments. It is also shown that the mixed-sign equilibria are contained in a ball of radius given by the norm of the positive equilibrium point and centered in the origin. Numerical examples are given to illustrate the results.

Place, publisher, year, edition, pages
2017. p. 781-786
Keywords [en]
Symmetric matrices, Eigenvalues and eigenfunctions, Bifurcation, Neural networks, Decision making, Steady-state, Cooperative systems
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-145192DOI: 10.1109/CDC.2017.8263755ISBN: 9781509028733 (electronic)ISBN: 9781509028726 (electronic)ISBN: 9781509028740 (print)OAI: oai:DiVA.org:liu-145192DiVA, id: diva2:1192590
Conference
2017 IEEE 56th Annual Conference on Decision and Control (CDC) December 12-15, 2017, Melbourne, Australia
Available from: 2018-03-22 Created: 2018-03-22 Last updated: 2019-05-09Bibliographically approved

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Investigating mixed-sign equilibria for nonlinear collective decision-making systems(372 kB)24 downloads
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Fontan, AngelaAltafini, Claudio

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Citation style
  • apa
  • harvard1
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  • Other style
More styles
Language
  • de-DE
  • en-GB
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