title: The Hindmarsh-Rose neuron model: bifurcation analysis and piecewise-linear approximations.
abstract: This paper provides a global picture of the bifurcation scenario of the Hindmarsh-Rose model. A combination between simulations and numerical continuations is used to unfold the complex bifurcation structure. The bifurcation analysis is carried out by varying two bifurcation parameters and evidence is given that the structure that is found is universal and appears for all combinations of bifurcation parameters. The information about the organizing principles and bifurcation diagrams are then used to compare the dynamics of the model with that of a piecewise-linear approximation, customized for circuit implementation. A good match between the dynamical behaviors of the models is found. These results can be used both to design a circuit implementation of the Hindmarsh-Rose model mimicking the diversity of neural response and as guidelines to predict the behavior of the model as well as its circuit implementation as a function of parameters.
authors.affiliation: Department of Biophysical and Electronic Engineering, University of Genoa, Via Opera Pia 11a, I-16145 Genova, Italy. marco.storace@unige.it
authors.forename: Marco
authors.initials: M
authors.lastname: Storace
authors.forename: Daniele
authors.initials: D
authors.lastname: Linaro
authors.forename: Enno
authors.initials: E
authors.lastname: de Lange
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000465:Algorithms; D000818:Animals; D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D006801:Humans; D016014:Linear Models; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*; D009435:Synaptic Transmission / Q000502:physiology