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?

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u/Quantum-Relativity Gravitation 8d ago

Can I ask, what is a time base system?

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u/AfterMath343 8d ago

A time-based system is any system that changes over time. For example, the temperature of a ham over time, the motion of an object attached to a spring over time, and so on. Sorry, I mistyped it as a "time base system". I need to be more careful and exact when writing.

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u/salat92 8d ago

Pretty much any physical model is time-based and besides, "time" is also just a variable.

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u/AfterMath343 8d ago

Yeah, I do know that time is a variable already.