Are fixed points and equilibria the same thing, in terms of a logistic map?
2026-04-28 10:54:50.1777373690
Are fixed points and equilibria the same thing?
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In short: yes. In a bit more detail:
In a discrete time dynamical system, call the current state $x$ and the next state $Tx$. You have equilibrium (the system staying in one place) exactly when $Tx=x$. This equation can be rephrased as "$x$ is a fixed point of $T$." So while an equilibrium and a fixed point are the same, they are different perspectives on the same thing. Fixed points of $T$ make sense even when we don't think about $T$ as forming a dynamical system.