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Haha, just because your dynamic system has an attractor does not mean the attractor is desirable.

"the have a tendency toward an attractor in state-space" Interesting, can you expand? What is state-space, by the way?

State-space is a very powerful mathematical way of modeling the "state" or configuration of dynamical systems, systems that change over time. An "attractor" is by definition a system configuration that things tend to over time, so what @pjheinz has said is not actually very interesting. Attractors need not be good things, they're just things.