Some remarks on local activity and local passivity

B. Garay, S. Siegmund, S. Trostorff, M. Waurick

Research output: Contribution to journalArticle

Abstract

We study local activity and its contrary, local passivity, for linear systems and show that generically an eigenvalue of the system matrix with positive real part implies local activity. If all state variables are port variables we prove that the system is locally active if and only if the system matrix is not dissipative. Local activity was suggested by Leon Chua as an indicator for the emergence of complexity of nonlinear systems. We propose an abstract scheme which indicates how local activity could be applied to nonlinear systems and list open questions about possible consequences for complexity.
LanguageEnglish
Article number1750057
Number of pages13
JournalInternational Journal of Bifurcation and Chaos
Volume27
Issue number4
DOIs
Publication statusPublished - 30 Apr 2017
Externally publishedYes

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Passivity
Nonlinear systems
Linear systems
Nonlinear Systems
Linear Systems
If and only if
Eigenvalue
Imply

Keywords

  • local activity
  • passivity
  • edge of chaos
  • instability
  • nonlinear systems

Cite this

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Some remarks on local activity and local passivity. / Garay, B.; Siegmund, S.; Trostorff, S.; Waurick, M.

In: International Journal of Bifurcation and Chaos, Vol. 27, No. 4, 1750057, 30.04.2017.

Research output: Contribution to journalArticle

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