Some Remarks on Local Activity and Local Passivity

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

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1 Citation (SciVal)


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.

Original languageEnglish
Article number1750057
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number4
Publication statusPublished - 1 Apr 2017


  • edge of chaos
  • instability
  • Local activity
  • passivity

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering(all)
  • General
  • Applied Mathematics


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