Parabolic bursting in an excitable system coupled with a slow oscillation
SIAM Journal on Applied Mathematics
Simulation of chaotic EEG patterns with a dynamic model of the olfactory system
Biological Cybernetics
Computing Hopf Bifurcations II: Three Examples from Neurophysiology
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Elements of applied bifurcation theory (2nd ed.)
Elements of applied bifurcation theory (2nd ed.)
Simulating, Analyzing, and Animating Dynamical Systems: A Guide Toi Xppaut for Researchers and Students
MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs
ACM Transactions on Mathematical Software (TOMS)
Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems
Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems
Bifurcation analysis of Jansen's neural mass model
Neural Computation
Dynamics and bifurcations of the adaptive exponential integrate-and-fire model
Biological Cybernetics - Special Issue: Quantitative Neuron Modeling
Numerical continuation of fold bifurcations of limit cycles in MATCONT
ICCS'03 Proceedings of the 1st international conference on Computational science: PartI
Simple model of spiking neurons
IEEE Transactions on Neural Networks
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In this letter, we propose a general framework for studying neural mass models defined by ordinary differential equations. By studying the bifurcations of the solutions to these equations and their sensitivity to noise, we establish an important relation, similar to a dictionary, between their behaviors and normal and pathological, especially epileptic, cortical patterns of activity. We then apply this framework to the analysis of two models that feature most phenomena of interest, the Jansen and Rit model, and the slightly more complex model recently proposed by Wendling and Chauvel. This model-based approach allows us to test various neurophysiological hypotheses on the origin of pathological cortical behaviors and investigate the effect of medication. We also study the effects of the stochastic nature of the inputs, which gives us clues about the origins of such important phenomena as interictal spikes, interictal bursts, and fast onset activity that are of particular relevance in epilepsy.