Homeorhesis, derived from the Greek

Greek language

Greek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...

 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

Homeostasis

Homeostasis is the property of a system that regulates its internal environment and tends to maintain a stable, constant condition of properties like temperature or pH...

.

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

Chreod

Chreod, is a portmanteau term coined by 20th century biologist Conrad Hal Waddington that combines the Greek word for "determined" or "necessary" and the word for "pathway." The term was used along with homeorhesis, which describes a system that returns to a steady trajectory in contrast to...

, meaning "necessary path", which is the trajectory to which the system tends to return.

Gaia hypothesis

In ecology

Ecology

Ecology is the scientific study of the relations that living organisms have with respect to each other and their natural environment. Variables of interest to ecologists include the composition, distribution, amount , number, and changing states of organisms within and among ecosystems...

 the concept is important as an element of the Gaia hypothesis

Gaia hypothesis

The Gaia hypothesis, also known as Gaia theory or Gaia principle, proposes that all organisms and their inorganic surroundings on Earth are closely integrated to form a single and self-regulating complex system, maintaining the conditions for life on the planet.The scientific investigation of the...

, where the system under consideration is the ecological balance of different forms of life on the planet. It was Lynn Margulis

Lynn Margulis

Lynn Margulis was an American biologist and University Professor in the Department of Geosciences at the University of Massachusetts Amherst. She is best known for her theory on the origin of eukaryotic organelles, and her contributions to the endosymbiotic theory, which is now generally accepted...

, the coauthor of Gaia hypothesis, 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.