Dynamics in hybrid complex systems of switches and oscillators

Dane Taylor, Elana J. Fertig, Juan G. Restrepo

Research output: Contribution to journalArticle

Abstract

While considerable progress has been made in the analysis of large systems containing a single type of coupled dynamical component (e.g., coupled oscillators or coupled switches), systems containing diverse components (e.g., both oscillators and switches) have received much less attention. We analyze large, hybrid systems of interconnected Kuramoto oscillators and Hopfield switches with positive feedback. In this system, oscillator synchronization promotes switches to turn on. In turn, when switches turn on, they enhance the synchrony of the oscillators to which they are coupled. Depending on the choice of parameters, we find theoretically coexisting stable solutions with either (i) incoherent oscillators and all switches permanently off, (ii) synchronized oscillators and all switches permanently on, or (iii) synchronized oscillators and switches that periodically alternate between the on and off states. Numerical experiments confirm these predictions. We discuss how transitions between these steady state solutions can be onset deterministically through dynamic bifurcations or spontaneously due to finite-size fluctuations.

Original languageEnglish (US)
Article number033142
JournalChaos
Volume23
Issue number3
DOIs
StatePublished - Jul 8 2013

Fingerprint

complex systems
Hybrid Systems
Large scale systems
Complex Systems
Switch
switches
Switches
oscillators
synchronized oscillators
positive feedback
Positive Feedback
Synchrony
Stable Solution
Coupled Oscillators
Steady-state Solution
Hybrid systems
Alternate
synchronism
Synchronization
Bifurcation

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Applied Mathematics

Cite this

Dynamics in hybrid complex systems of switches and oscillators. / Taylor, Dane; Fertig, Elana J.; Restrepo, Juan G.

In: Chaos, Vol. 23, No. 3, 033142, 08.07.2013.

Research output: Contribution to journalArticle

Taylor, Dane ; Fertig, Elana J. ; Restrepo, Juan G. / Dynamics in hybrid complex systems of switches and oscillators. In: Chaos. 2013 ; Vol. 23, No. 3.
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