Simulation of chaotic EEG patterns with a dynamic model of the olfactory system
Biological Cybernetics
Differential equations and dynamical systems
Differential equations and dynamical systems
Weakly connected neural networks
Weakly connected neural networks
Elements of applied bifurcation theory (2nd ed.)
Elements of applied bifurcation theory (2nd ed.)
Modeling Synchronization Loss in Large-Scale Brain Dynamics
ICANN '08 Proceedings of the 18th international conference on Artificial Neural Networks, Part II
Neural mass activity, bifurcations, and epilepsy
Neural Computation
Journal of Computational Neuroscience
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We present a mathematical model of a neural mass developed by a number of people, including Lopes da Silva and Jansen. This model features three interacting populations of cortical neurons and is described by a six-dimensional nonlinear dynamical system. We address some aspects of its behavior through a bifurcation analysis with respect to the input parameter of the system. This leads to a compact description of the oscillatory behaviors observed in Jansen and Rit (1995) (alpha activity) and Wendling, Bellanger, Bartolomei, and Chauvel (2000) (spike-like epileptic activity). In the case of small or slow variation of the input, the model can even be described as a binary unit. Again using the bifurcation framework, we discuss the influence of other parameters of the system on the behavior of the neural mass model.