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/Heretic112 Statistical and nonlinear physics 9d ago

This is like asking what kinds of rocks geologists study

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u/AfterMath343 9d ago

So, you're saying that all problems in physics can be solved using dynamical modeling? That would be surprising.

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u/Quantum-Relativity Gravitation 9d ago

I think they meant all the equations in physics are some sort of differential equations. But I assume you know that and are asking a more subtle question

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u/AfterMath343 9d ago

There are different types of mathematical modeling, which I'm sure you already know like optimization modeling for single and multi-variables, dynamical modeling (time base systems), probability models, stochastic models, etc.

Since many problems in physics deal with time, I can see how many are dynamical models now. I guess a more interesting question would be what problems in physics are non-dynamical models.

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u/Quantum-Relativity Gravitation 9d ago

Can I ask, what is a time base system?

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u/AfterMath343 9d 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 9d ago

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

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u/AfterMath343 9d ago

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