Neural mass model developed by Lopes da Silva et al. is able to describe limit cycle behavior in Electroencephalography (EEG) of alpha rhythm and exhibit complex dynamics between cortical areas. In this work, we extend Grimbert and Faugeras's work to study the dynamical behavior caused by interaction of cortical areas. The model is developed with the coupling of two neural populations. We show that various attractors, including equilibrium points, periodic solutions and chaotic strange attractors, could coexist in different ways with different value of the connectivity parameters. The main findings are that: (1) The stable equilibrium points only appear with a small value of the parameter. (2) While the alpha activities always exist for both two populations with proper initial conditions. Interestingly, the coexistence of the multiple alpha-to-epileptic activities implies the multiple coupling ways for these activities in phase. Two neuronal populations with epileptic activities could interact with multiple rhythms depending on their connectivity. (3) For particular interest, chaotic behaviors are identified in four regions divided by the connectivity parameter with the positive maximal Lyapunov exponent. The four types of chaotic attractors have their own structures, but all of them are related to the epileptic activities.
Bibliographical noteFunding Information:
This work is supported by National High Technology Research and Development Program of China ( no. 2009AA04Z212 ), Research Fund for the Doctoral Program of Higher Education of China ( no. 20090073120047 ), and National Natural Science Foundation of China ( no. 51075265 ).
- Neural mass model