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Periodically forced leaky integrate-and-fire model.

K Pakdaman1

  • 1Inserm U444, Faculté de Médecine Saint-Antoine, 27 Rue Chaligny, 75571 Paris Cedex 12, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
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This study reveals that leaky integrate-and-fire models with periodic forcing exhibit predictable discharge patterns. Regardless of the input type, the model

Area of Science:

  • Computational Neuroscience
  • Theoretical Neuroscience
  • Dynamical Systems

Background:

  • Leaky integrate-and-fire (LIF) models are fundamental in neuroscience for simulating neuronal firing.
  • Previous research primarily focused on LIF model responses to sinusoidal periodic inputs.
  • Understanding responses to arbitrary periodic inputs is crucial for broader applicability.

Purpose of the Study:

  • To analyze the discharge patterns of LIF models under arbitrary periodic forcing.
  • To generalize findings beyond sinusoidal stimulation.
  • To characterize the range of possible firing behaviors.

Main Methods:

  • Mathematical analysis of the phase map relating consecutive discharge times.
  • Characterization of the phase map as a piecewise continuous, orientation-preserving circle map.

Related Experiment Videos

  • Application of dynamical systems theory to analyze the map's properties.

    • Main Results:

    • The phase map is shown to be a circle map for any periodic input.
    • This implies a well-defined rotation number, independent of initial conditions.
    • Four distinct response types are identified: phase locking, quasiperiodic discharges, nonchaotic aperiodic firing, and finite-time termination.

    Conclusions:

    • The discharge dynamics of periodically forced LIF models are universally classifiable.
    • The model's response is constrained to one of four patterns irrespective of the specific periodic input.
    • This provides a robust framework for understanding neuronal firing under periodic influences.