T

where e is the matrix exponential (Bossel 1992). In this model, the system's behavior has two separable components: intrinsically sustained dynamics (parameterized by matrix A) and dynamics enforced by external inputs (parameterized by matrix C). The first term of (6) says that the change of the state variable Xi is a linear mixture of all state variables in the system, weighted by the parameters aij. By defining a particular parameter aij to be zero, we disallow for a direct effect of Xj on xi (see Fig. 1 for an example). Conversely, any non-zero parameter aij represents a causal influence of the dynamics of Xj on that of xi. The binarized parameter matrix A

X(aii) • • • x(ain) X(anl) • • • X(0nn).

represents the structural connectivity of the system model (see the chapter by Sporns & Tononi in this volume on how patterns of anatomical connections constrain effective connectivity and thus the dynamics of neural systems). The definition of the structural connectivity is usually guided by anatomical investigations in primates (Stephan et al. 2001b, Kotter 2004; see the chapter x u n m x

0 0

Post a comment