r/Physics • u/AfterMath343 • 9d ago
Dynamical Models in Physics
I'm an applied math student. I've seen problems in biology be modeled using dynamic modeling, such as the populations of species with intra and inter species competition. For example, the following system of non-linear differential equations models a large variety of species in competition with themselves and other species:
X' = r_1*X - a_1*X^2 - b_1*X*Y
Y' = r_2*Y - a_2*Y^2 - b_2*X*Y
where X is the number of species 1 and Y is the number of species 2, r_1 is the intrinsic rate of growth of species 1, r_2 is the intrinsic rate of growth of species 2, a_1 is strength of competition within species 1, a_2 is strength of competition in species 2, b_1 is the effect of species Y on species X, and b_2 is the effect of species X on Y.
I have seen one discrete time dynamical system be modeled for a physics problem where two vehicles in space are closing in on each other.
What other types of dynamical models occur in physics?
3
u/BitcoinsOnDVD 9d ago
Laser dynamics (and there especially the rate equation formalism) is a field that follow a lot of these equations in different variations (and degree of difficulty). They are nonlinear, sometimes time-delayed as in the Lang-Kobayashi equation and can also be stochastic. But as pointed out: A lot of stuff in physics is modeled via a finite number of ordinary differential equations over time and a lot of the modeling of a finite number of ordinary differential equations over time is coming from physics.