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Encyclopedia of Computational Neuroscience pp 1–7Cite as

Delay-Induced Transient Oscillation (DITO) and Metastable Behavior

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Definition

Delay-induced transient oscillations (DITOs) are oscillations that occur in bi- or multi-stable system of delayed differential equations as it converges to one of its stable equilibria, oscillations that do not exist when the delay vanishes.

Metastable oscillations are transient oscillatory patterns (or states) that attract neighboring initial conditions and last for a “long time” almost without change. These oscillatory patterns seem to be stable: to detect their instability, it is necessary to observe the system over a seemingly endless time window. Such long-lasting transients would be undistinguishable from (nearly) periodic solutions. A mathematical definition of metastability needs a quantification of “long time”. The most common approach is to consider a one-parameter family of systems and to compare the transient time duration for different values of the parameter. For instance, if ε >0 is a real parameter, then an oscillatory pattern is said to be metastable if...

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Author information

Authors and Affiliations

  1. Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brazil

    Clodoaldo Grotta-Ragazzo

  2. Instituto de Física, Universidade de São Paulo, São Paulo, Brazil

    Coraci P. Malta

  3. Institut Jacques Monod, Univ Paris Diderot, Paris, France

    Khashayar Pakdaman

Authors
  1. Clodoaldo Grotta-Ragazzo
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  2. Coraci P. Malta
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  3. Khashayar Pakdaman
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Corresponding author

Correspondence to Coraci P. Malta .

Editor information

Editors and Affiliations

  1. Atlanta, GA, USA

    Dieter Jaeger

  2. Department of Biomedical Engineering, Florida International University, Miami, FL, USA

    Ranu Jung

Section Editor information

  1. W.M. Keck Science Center, The Claremont Colleges, Claremont, CA, USA

    John Milton Professor of Biology

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Grotta-Ragazzo, C., Malta, C.P., Pakdaman, K. (2019). Delay-Induced Transient Oscillation (DITO) and Metastable Behavior. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_100678-1

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  • DOI: https://doi.org/10.1007/978-1-4614-7320-6_100678-1

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-7320-6

  • Online ISBN: 978-1-4614-7320-6

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