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The Hindmarsh-Rose neuron model: bifurcation analysis and piecewise-linear approximations
Marco Storace1, Daniele Linaro, Enno de Lange
1Department of Biophysical and Electronic Engineering, University of Genoa, Via Opera Pia 11a, I-16145 Genova, Italy. marco.storace@unige.it
Chaos (Woodbury, N.Y.)
|December 3, 2008
Summary
This study reveals universal bifurcation structures in the Hindmarsh-Rose model, crucial for understanding neural dynamics. These findings aid in designing accurate circuit implementations that mimic diverse neural responses.
Area of Science:
- Computational Neuroscience
- Dynamical Systems Theory
- Circuit Design
Background:
- The Hindmarsh-Rose model is a fundamental mathematical model used to simulate the behavior of neurons.
- Understanding the complex dynamics and parameter-dependent behaviors of such models is essential for neuroscience research and applications.
- Previous studies have explored various aspects of the Hindmarsh-Rose model, but a comprehensive global bifurcation analysis was lacking.
Purpose of the Study:
- To provide a global picture of the bifurcation scenario of the Hindmarsh-Rose model.
- To investigate the universality of its bifurcation structure across different parameter combinations.
- To compare the model's dynamics with a piecewise-linear approximation for circuit implementation.
Main Methods:
- Utilized a combination of numerical simulations and numerical continuation techniques.
- Performed bifurcation analysis by systematically varying two key bifurcation parameters.
- Compared the dynamical behaviors of the original Hindmarsh-Rose model with a piecewise-linear approximation.
Main Results:
- Uncovered a complex, yet universal, bifurcation structure within the Hindmarsh-Rose model.
- Demonstrated that this bifurcation structure is consistent across all combinations of the analyzed bifurcation parameters.
- Found a good match between the dynamical behaviors of the original model and its piecewise-linear approximation.
Conclusions:
- The identified universal bifurcation structure provides a framework for predicting model behavior.
- The findings facilitate the design of accurate circuit implementations of the Hindmarsh-Rose model.
- These results enable the mimicry of diverse neural response patterns in artificial systems.
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