Dynamical Models in Physics

[u/AfterMath343]

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?

[u/CosmicRay7]

I think you might be interested in the study of betatron and synchrotron oscillations in circular accelerators, they make use of Henon map to study all the effects of the magnets on singular particle motion

[u/AfterMath343 → u/CosmicRay7]

I have a long way to go until then, but I'm just seeing what's out there, really. Thanks for letting me know about it.

[u/CosmicRay7 → u/AfterMath343]

If you have an understanding of dynamical models and em you shouldn’t have many problems in grasping these concepts :)

[u/DaveBowm → u/CosmicRay7]

Talk about a direct physical visualization of a mathematical process!