Skip to main content
SpringerLink
Log in

Delay-Induced Transient Oscillation (DITO) and Metastable Behavior

  • Living reference work entry
  • First Online:
Encyclopedia of Computational Neuroscience

  • 154 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

References

  • an der Heiden U (1981) Analysis of neural networks. Lecture notes in biomathematics, vol 35. Springer, Berlin

    Google Scholar 

  • Chapeau-Blondeau F, Chauvet G (1992) Stable, oscillatory, and chaotic regimes in the dynamics of small neural networks with delay. Neural Netw 5:735–743

    Article  Google Scholar 

  • Chow S-N, Mallet-Paret J (1983) Singularly perturbed delay-differential equations. North-Holland Math Stud 80:7–12

    Article  Google Scholar 

  • Diez-Martínez O, Segundo JP (1983) Behavior of a single neuron in a recurrent excitatory loop. Biol Cybern 47:33–41

    Article  Google Scholar 

  • Foss J, Longtin A, Mensour B, Milton J (1996) Multistability and delayed recurrent loops. Phys Rev Lett 76:708–711

    Article  CAS  Google Scholar 

  • Fusco G, Hale JK (1989) Slow-motion manifolds, dormant instability, and singular perturbations. J Dyn Diff Equat 1:75–94

    Article  Google Scholar 

  • Grotta-Ragazzo C, Pakdaman K, Malta CP (1999) Metastability for delayed differential equations. Phys Rev E 60:6230–6233

    Article  CAS  Google Scholar 

  • Grotta-Ragazzo C, Malta CP, Pakdaman K (2010) Metastable periodic patterns in singularly perturbed delayed equations. J Dyn Diff Equat 22:203–252

    Article  Google Scholar 

  • Hangartner RD, Cull P (1995) A ternary logic model for recurrent neuromine networks with delay. Biol Cybern 73:177–188

    Article  CAS  Google Scholar 

  • Hirsch MW (1989) Convergent activation dynamics in continuous time networks. Neural Netw 2:331–350

    Article  Google Scholar 

  • Hopfield JJ (1984) Neurons with graded response have collective computational properties like those of two-state neurons. Proc Natl Acad Sci USA 81:3088–3092

    Article  CAS  Google Scholar 

  • Ikeda K, Matsumoto K (1987) High-dimensional chaotic behavior in systems with time-delayed feedback. Phys D 29:223–235

    Article  Google Scholar 

  • Lourenço C, Babloyantz A (1994) Control of chaos in networks with delay: a model for synchronization of cortical tissue. Neural Comput 6:1141–1154

    Article  Google Scholar 

  • Menon V (1995) Interaction of neuronal populations with delay: effect of frequency mismatch and feedback gain. Int J Neural Syst 6:3–17

    Article  CAS  Google Scholar 

  • Milton J, Naik P, Chan C, Campbell SA (2010) Indecision in neural decision making models. Math Model Nat Phenom 5:125–145

    Article  Google Scholar 

  • Milton J, Wu J, Campbell SA, Bélair J (2017) Outgrowing neurological diseases: microcircuits, conduction delay and childhood absence epilepsy. In: Computational neurology and psychiatry. Springer, Cham, pp 11–47

    Chapter  Google Scholar 

  • Pakdaman K, Malta CP (1998) A note on convergence under dynamical thresholds with delays. IEEE Trans Neural Netw 9:231–233

    Article  CAS  Google Scholar 

  • Pakdaman K, Vibert J-F, Boussard E, Azmy N (1996) Single neuron with recurrent excitation: effect of the transmission delay. Neural Netw 9:797–818

    Article  Google Scholar 

  • Pakdaman K, Malta CP, Grotta-Ragazzo C, Arino O, Vibert J-F (1997a) Transient oscillations in continuous-time excitatory ring neural networks with delay. Phys Rev E 55:3234–3247

    Article  CAS  Google Scholar 

  • Pakdaman K, Malta CP, Grotta-Ragazzo C, Vibert J-F (1997b) Effect of delay on the boundary of the basin of attraction in a self-excited single graded-response neuron. Neural Comput 9:319–336

    Article  CAS  Google Scholar 

  • Pakdaman K, Grotta-Ragazzo C, Malta CP (1997c) Delay-induced transient oscillations in a two-neuron network. Res. Inst. Matem e Estat. da USP 3:45–54

    Google Scholar 

  • Pakdaman K, Malta CP, Grotta-Ragazzo C, Arino O, Vibert J-F (1998a) Effect of delay on the boundary of the basin of attraction in a system of two neurons. Neural Netw 11:509–519

    Article  Google Scholar 

  • Pakdaman K, Grotta-Ragazzo C, Malta CP (1998b) Transient regime duration in continuous-time neural networks with delay. Phys Rev E 58:3623–3627

    Article  CAS  Google Scholar 

  • Pakdaman K, Malta CP, Grotta-Ragazzo C (1999) Asymptotic behavior of irreducible excitatory networks of analog graded-response neurons. IEEE Trans Neural Netw 10:1375–1381

    Article  CAS  Google Scholar 

  • Pellegrin X, Grotta-Ragazzo C, Malta CP, Pakdaman K (2014) Metastable periodic patterns in singularly perturbed state-dependent delayed equations. Phys D 271:48–63

    Article  Google Scholar 

  • Plant RE (1981) A FitzHugh differential–difference equation modeling recurrent neural feedback. SIAM J Appl Math 40:150–162

    Article  Google Scholar 

  • Segundo JP, Stiber M, Altshuler E, Vibert J-F (1994) Transients in the inhibitory driving of neurons and their postsynaptic consequences. Neuroscience 62:459–480

    Article  CAS  Google Scholar 

  • Sharkovsky AN, Maistrenko YL, Romanenko EY (1993) Difference equations and their applications. Kluwer Academic Publishers, Dordrecht

    Book  Google Scholar 

  • Vibert J-F, Davis M, Segundo JP (1979) Recurrent inhibition: its influence upon transduction and afferent discharges in slowly-adapting stretch receptor organs. Biol Cybern 33:167–178

    Article  CAS  Google Scholar 

  • Vibert J-F, Pakdaman K, Azmy N (1994) Interneural delay modification synchronizes biologically plausible neural networks. Neural Netw 7:589–607

    Article  Google Scholar 

Download references

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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Coraci P. Malta
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Khashayar Pakdaman
    View author publications

    You can also search for this author in PubMed Google Scholar

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

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Science+Business Media, LLC, part of Springer Nature

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

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

Download citation

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

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-7320-6

  • Online ISBN: 978-1-4614-7320-6

  • eBook Packages: Springer Reference Biomedicine and Life SciencesReference Module Biomedical and Life Sciences

Publish with us

Policies and ethics

Search

Navigation