Homeorhesis, derived from the Greek for "similar flow", is a concept encompassing dynamical systems which return to a trajectory, as opposed to systems which return to a particular state, which is termed homeostasis.

Biology

The word itself is a little-used term of art in biology, where it describes the tendency of developing or changing organisms to continue development or change towards a given state, even if disturbed in development. The term was first coined by C.H. Waddington, on or before 1940, along with the related term chreod, meaning "necessary path", which is the trajectory to which the system tends to return.

Gaia Theory

In ecology the concept is important as an element of the Gaia theory, where the system under consideration is the ecological balance of different forms of life on the planet. It was Lynn Margulis, the coauthor of Gaia hypotheses, who wrote in particular that only homeorhetic and not homeostatic balances are involved in the theory. That is, the composition of Earth's atmosphere, hydrosphere, and lithosphere are regulated around "set points" as in homeostasis, but those set points change with time.