That kind of chaos is about simple systems that are unpredictable in the long term. That Lorenz system is just a few equations you could write on a napkin. Whereas your brain has billions and billions of neurons. (You might blame the complexity on having a lot of parts.)
That said, another aspect of dissipative chaos is that a highly complex system like turbulence (10^28 or so atoms bouncing off each other) often can be described by an attractor that is rather low dimensional and could be modeled with a few equations. So you might have some neural signal that tools like that could make an interesting model of.
as long as the dynamics are relatively low dimensional, it should be possible to estimate the differential equation, even if it is observed in a high dimensional space
That said, another aspect of dissipative chaos is that a highly complex system like turbulence (10^28 or so atoms bouncing off each other) often can be described by an attractor that is rather low dimensional and could be modeled with a few equations. So you might have some neural signal that tools like that could make an interesting model of.