Complex behavior in a modified Jansen and Rit neural mass model
© Spiegler et al; licensee BioMed Central Ltd. 2011
Published: 18 July 2011
Neural mass models (NMM) explain dynamics of neuronal populations and were designed to strike a balance between mathematical simplicity and biological plausibility . It has been demonstrated that, even in the absence of any time-variant input, they are capable of producing a number of biologically relevant behavior . However, cortical input is often periodic, since neural ensembles tend to oscillate intrinsically or due to rhythmic external stimuli . Here, we investigate the Jansen and Rit NMM for a cortical area , comprising three neural masses for pyramidal cells and inhibitory and excitatory interneurons, in response to periodic stimulus of varying frequency.
We consider periodic pulse-like input and systematically vary the normalized input frequency between >0 and 18.5·10–2 around the intrinsic frequency (10.8·10–2) of the unperturbed NMM (arising from Andronov-Hopf bifurcations) . The normalized stimulus amplitude (ζ = 1.5) is located within the effective extrinsic input range . The parameter space is charted by means of Lyapunov spectra, Kaplan-Yorke dimension, time series and power spectra.
We conclude that a periodically forced Jansen and Rit NMM can yield very complex dynamics, including chaos, for plausible parameters. Such complex behavior could explain multi-stability in M/EEG data, which can be observed, for instance, in perception (e.g., binocular rivalry), stages of sleep, changes in attention or vigilance, progression of diseases (e.g., epilepsy), and effects of medication. As an example, we have shown that this model reproduces the resonance phenomena in a clinically relevant photic driving experiment .
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