Brands as Attractors

So all this talk of brands and identities makes me wonder if we shouldn't view brands as attractors. Now I'm going to have to be careful here because when I say attractor, I don't mean "magnet". I mean attractor more like this explanation from wikipedia.

An attractor is a set to which a dynamical system evolves after a long enough time. That is, points that get close enough to the attractor remain close even if slightly disturbed. Geometrically, an attractor can be a point, a curve, a manifold, or even a complicated set with a fractal structure known as a "strange attractor".

Note that an attractor is where a system tends to end up. Move the elements of the system away from that and they return to it. The attractor does not exist independently but as an aspect of the system. In particular, the patterns formed by the strange attractors of chaotic systems are in constant motion, indicating a system that never reaches repose but is both describable & beautiful.

In a similar way, organisations do not have complete control over their brands - but they are actors within the system. The brand is where their behaviour ends up. Other participants within the system may also end up there - and may also change the nature of the system. Just as strange attractors may whirl in motion around multiple points so the identity of an organisation & its outputs may oscillate around multiple identities (caring, ruthless, efficient, etc).

I realise I am probably bastardising precise science with unwarranted speculation but what the hell, it's Saturday night.

I'd like to lock some mathematicians and marketers in a room to nut this one out but it may end with mutual sniping around partial differential equations and personal hygiene. Still it could be worth a shot - any volunteers?