Fig. 32. Exponential coupling function x
Fig. 32. Exponential coupling function system. It is notable that Nunez's approach represents the first attempt to use structural information to constrain the neural field dynamics for the large scales observed in encephalographic measurements. His consideration of the corticocortical fiber system within the integral kernel of (49) has influenced much of the later research in the field of EEG and MEG (Jirsa & Haken 1996,1997; Wright and Liley 1996; Jirsa et al. 1998, 2002; Robinson et al. 1997, 2001; Steyn-Ross et al. 1999 ; Breakspear et al. 2006) and lead to the development of neural field dynamics for large scale systems.
Wilson & Cowan (1972) initially considered the interaction of two populations of excitatory and inhibitory nature characterized by their firing rates ^i(t) and ^2(t). An der Heiden (1980) showed nicely the connection between the local Wilson-Cowan population model (1972) and the McCulloch-Pitts model (1943). Later Wilson and Cowan (1973) extended their model to two layers of coupled neural fields ^1(x,t) and ^2(x,t) (see Fig. 33) obeying the following equation
where we use the same notation as in the Nunez model. Various dynamic phenomena were found as a function of the connectivity h including steady network states, standing and traveling waves. An emphasis was placed on the spatial localization of activations, which functionally necessitated the constraint that inhibitory connections are of longer range than excitatory interactions. Such is in analogy to Amari's model and is anatomically reflected in the longer axons of inhibitory interneurons. This constraint, however, requires
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