#Emergence: PLEASEE HELP

8 messages · Page 1 of 1 (latest)

heady lance
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Heyy, so I need to do this for an assignment on modeling and complexity. this is a simplified version of the problem I'm trying to prove:

If I have an equation like E(t) = he^g(t)t/ke^t

with g(t) = bt + h

and I want to show convergence of two instances of E(t) (say E_a and E_b), then I can say

as t --> infinity the plateaus of E_b and E_a will be the same: h_a = h_b

using g(t) I can write something like
g_a(t) - b_at = g_b(t)-b_bt

and find a relationship between the parameters so that this is fulfilled.
But that doesn't show that E_a and E_b plateauing at the same level is an emergent property. How can I model this system to make this an emergent property?

📎 crap.pdf
sharp capeBOT
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heady lance
sharp capeBOT
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@heady lance

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boreal scaffold
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It’s worth noting that by using the properties of exponents, you can write this as (h/k)e^(t(g(t)-1)), and so everything is of a much simpler class than indicated. But convergence depends only on if b>0 (or a different condition if b=0), in which case it converges to 0.

But i don’t fully understand what you’re asking, so I don’t know if this is helpful.

lyric idol
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@heady lance someone answered

heady lance