Periodically forced neural mass model: entrainment and complex behavior
© Spiegler et al; licensee BioMed Central Ltd. 2010
Published: 20 July 2010
Neural mass models (NMM) provide a parsimonious, yet biophysically plausible, way to model mass action in the nervous system . 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 . Moreover, by slowly traversing the parameter space, they can serve as generative models for ordered sequences of oscillatory regimes observed in EEG or MEG data . In the brain, neural circuits are embedded in global networks and may experience high amplitude input from other areas. Such input is very often periodic. Here, we systematically investigate the behavior of a NMM of a cortical area, comprising three neural masses for pyramidal cells and inhibitory and excitatory interneurons, in response to periodic input, as a function of input amplitude and frequency.
In our previous work we studied the system with constant input . Two mechanisms for oscillations could be identified: homoclinic and Hopf cycles. Here, we extend our study by considering periodic pulse-like input and systematically vary amplitude and frequency of the input for the widely used parameter set proposed by Jansen and Rit . The input frequency ranges between 4 Hz and 19 Hz including the intrinsic frequency (correponding to the Hopf cycle), and the amplitude values are 1/3, 2/3, 1, 4/3 and 5/3 of amplitude of the Hopf cycle in the unperturbed system. We study the phase space orbits and the time evolution of all variables. The largest Lyapunov exponents and the spectra of the time series are calculated. For studying the relationship of system input and response we compute the frequency-detuning curves, i.e., the frequency difference of response and input plotted against the input frequency.
For the first time we found complicated behavior like entrainment, chaos, quasi- and multi-periodicity in a neural mass model by using periodic input. Hence, this NMM may be capable of serving as a generative model for much more complex and diverse phenomena than previously thought.
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