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Two-state Markovian theory of input–output frequency and phase synchronization

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  • Casado-Pascual, Jesús
  • Gómez-Ordóñez, José
  • Morillo, Manuel

Abstract

A Markovian dichotomic system driven by a deterministic time-periodic force is analyzed in terms of the statistical properties of the switching events between the states. The consideration of the counting process of the switching events leads us to define a discrete phase. We obtain expressions for the instantaneous output frequency and phase diffusion associated to the dichotomic process, as well as for their cycle averages. These expressions are completely determined by the rates of escape from both states. They are a convenient starting point for the study of the stochastic frequency and phase synchronization in a wide range of situations (both classical and quantum) in which two metastable states are involved.

Suggested Citation

  • Casado-Pascual, Jesús & Gómez-Ordóñez, José & Morillo, Manuel, 2005. "Two-state Markovian theory of input–output frequency and phase synchronization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 351(1), pages 117-125.
    • Handle: RePEc:eee:phsmap:v:351:y:2005:i:1:p:117-125
    DOI: 10.1016/j.physa.2004.12.013
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    References listed on IDEAS

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    1. Prager, T & Naundorf, B & Schimansky-Geier, L, 2003. "Coupled three-state oscillators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 325(1), pages 176-185.
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