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Chaotic oscillations in a map-based model of neural activity
M Courbage1, V I Nekorkin, L V Vdovin
1Laboratoire Matière et Systèmes Complexes, UMR 7057, CNRS et Université Paris 7-Denis Diderot, Batiment Condorcet 75205 Paris Cedex 13, France.
Chaos (Woodbury, N.Y.)
|January 1, 2008
Summary
We developed a new discrete time dynamical system model for excitable neurons. This model exhibits chaotic spiking-bursting oscillations and other neural activities.
Area of Science:
- Computational Neuroscience
- Mathematical Biology
- Dynamical Systems Theory
Background:
- Understanding the complex dynamics of neurons is crucial for neuroscience.
- Existing models often simplify or fail to capture the full range of neural behaviors.
- Excitable and spiking-bursting neuronal activity underlies various brain functions.
Purpose of the Study:
- To propose a novel discrete time dynamical system (map) as a phenomenological model for excitable and spiking-bursting neurons.
- To investigate the conditions for chaotic attractors within this model.
- To demonstrate the model's ability to reproduce diverse neural activity patterns.
Main Methods:
- Development of a discontinuous two-dimensional discrete time map.
- Analysis of the phase plane to identify invariant regions.
- Characterization of the chaotic attractor and its generated oscillations.
- Simulation of various neural activity regimes.
Main Results:
- Identification of conditions leading to an invariant region containing a chaotic attractor.
- Demonstration of chaotic spiking-bursting oscillations generated by this attractor.
- Observation of other neural activities, including subthreshold oscillations and phasic spiking, from the model.
Conclusions:
- The proposed discrete time map serves as an effective phenomenological model for excitable neurons.
- The model successfully generates chaotic spiking-bursting activity and other relevant neural dynamics.
- This framework offers a new tool for studying complex neuronal behavior computationally.
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