[Maths] Daisyworld [Help]

[Appocomaster]

Those of you who remember me saying all that time ago I was going to do a Cryptography project: I lied. I'm doing Daisyworld.
It's not looking too bad, but after analysing the steady states (which is even in the paper and just has to be reworded and explained), I have to do a proper analysis in terms of it as a dynamical system. I have some idea of how to do it (my supervisor gave me a prod and I did a module on it last term) but it's a bit confusing as apparently I need to analyse 8 equations or so to find the fixed points of the system.

The "steady state analysis" seems to do this for d/dt(a_{w})= 0 and d/dt(a_{b})=0, for x and B constant. What I don't get is how I include all the other equations for when x and B are variables (x = p - a_{w} - a_{b}, B = growth rate).
No, wikipedia is no use. In fact, none of the pages I've found are of any use. Neither is the library, it seems. It's all so confusing

(no bets as to whether MrL_JaKiri will post on this thread :P)

[MrL_JaKiri]

Could you define your terms, and what the argument that you're putting forward is (it makes it much easier to analyse)?

[Nodrog]

I've no idea what youre talking about and you need to learn how to become better at asking questions.

[MrL_JaKiri]

Originally Posted by Nodrog

I've no idea what youre talking about and you need to learn how to become better at asking questions.

Daisyworld is a modelling exercise where you take a planet which can have three kinds of surfaces: uncovered, black dasies and white dasies. They require different conditions to grow, and the amount of each affects the conditions.

[queball]

You just have to count the dots around the edge whenever there's a dot in the middle.

[Appocomaster]

http://nrich.maths.org/MOTIVATE/conf16/

the equations as specified http://nrich.maths.org/MOTIVATE/conf16/PSaunders6.gif


However, having read it, I see that it at hints at the step in the right direction. It does ignore the steady state analysis done in the original paper (which is in some ways more basic) but I do understand it, as far as it goes.

I understand how to get Tb, but then he stops and I get confused. Do you just plug that value of Tb into everything else? and then plot L against Tb (or Te?)
I can do it for no daisys. It's when you get daisys it gets complicated.

[Appocomaster]

Originally Posted by queball

You just have to count the dots around the edge whenever there's a dot in the middle.

That's the flower thing

[Deepflow]

I endorse this thread in so far as to say that I had never heard of daisyworld but i wikied it and read the article and it's actually quite interesting.

I know nothing about the maths though, sorry appocco.

[Appocomaster]

the basic idea is that life "automatically" causes stability in it's environment, and works against external changes. It's sort of like a closed chemical system which is slowly changed (for example two gasses in a glass tube that varies size change their equilibrium to best suit how long the tube is)

[Deepflow]

I found the most interesting part the bit about increased biodiversity adding greater stability.

Are you going to add more than daisies to the simulation?

[Appocomaster]

Originally Posted by Deepflow

I found the most interesting part the bit about increased biodiversity adding greater stability.

Are you going to add more than daisies to the simulation?

No. cos I'm lazy and analysing it. For some reason, modelling it in 3d also adds more stability (although iirc, it oscillates as opposted to having a steady state)