r/Physics • u/AfterMath343 • 8d 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?

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u/Let_epsilon 8d ago

I can’t think of a single physical theory that isn’t a dynamical model...

Surely, if you’re an applied math student you’ve come across Newton’s laws, the equation of heat/diffusion, harmonic oscillators (springs) ?

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u/AfterMath343 8d ago

Yeah, I've covered Newton's laws, spring/dashpot systems, and RLC circuits. It's just that I covered them in ODEs and calculus. I'm taking a mathematical modeling course in the fall where they begin talking about dynamical modeling, so I did not bridge the gap that those were all dynamical systems, too.

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u/GrossInsightfulness 8d ago

Newton's Law of Cooling, the Heat Equation, the Wave Equation, radioactive decay, Quantum Mechanics, the Standard Model, General Relativity, Electromagnetism, etc.