From Osher Doctorow
In other words, the Riccati Differential Equation in its exponential
growth/decay or expansion/contraction subtype is the "natural"
equation for radial expansion/contraction as opposed to tangential
motion which is usually "one direction at a time type", as I've
discussed many times in previous postings, with tangential motion
typically given by the usual dynamical equations.
When the expanding or contracting object is an extended body, the body
can be regarded as simultaneously "deciding" to expand or contract to
a certain degree or magnitude in each direction, and these can all be
different or some can be similar, unlike tangential motion which is
not simultaneous but in one direction at a time.
This is why, in Cosmological Physics, in my view the Riccati
Differential Equation is the main equation to use, although it can
arguably be generalized to partial differential equation(s) or systems
of equations somewhat analogously to the Lotka-Volterra equations.
The Logistic Differential Equation is another Riccati subtype of
considerable importance in science.
Osher Doctorow
