A Linear Analysis of Coupled Wilson-Cowan Neuronal Populations

Figure 2

Temporal evolutions of obtained by numerically integrating (2). In all cases, the initial condition is the origin of the state space. In all cases, , , , , , , and . In (a), , ; in (b), , ; in (c), , , and ; in (d), , , and ; in (e), , , , and ; in (f), , , and ; in (g), , , and ; in (h), , , and ; and in (i), , , and . In (a) and (c), the system converges to an equilibrium point; in (b), (d), (e), (g), and (i) to a limit cycle; in (f) to a two-dimensional torus; and in (h) to a chaotic attractor.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)