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What is the characteristic of "steady-state"?View attachment 20741

Anyone able to work out this steady state question?

Please show us what you have tried and *exactly where you are stuck*.

Please follow the rules of posting in this forum, as enunciated at:

Please share your work/thoughts about this problem.

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sorry, I wasn't aware of the rules. So it's the wording of "as a function of E" that I'm not entirely sure with. I know for a steady state you want to set du/dt to 0. So my working out is as follows:What is the characteristic of "steady-state"?

Please show us what you have tried andexactly where you are stuck.Please follow the rules of posting in this forum, as enunciated at:Please share your work/thoughts about this problem.

View attachment 20742

0=u*(1-u*)(1+u*)-Eu*

Eu*=u*(1-u*)(1+u*)

E=(1-u*)(1+u*)

Giving u*=1-E or u*=E-1

Any feedback on this would be great, thanks

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No!sorry, I wasn't aware of the rules. So it's the wording of "as a function of E" that I'm not entirely sure with. I know for a steady state you want to set du/dt to 0. So my working out is as follows:

0=u*(1-u*)(1+u*)-Eu*

Eu*=u*(1-u*)(1+u*)

E=(1-u*)(1+u*)

Giving u*=1-E or u*=E-1.............................................How are you getting these?!

Any feedback on this would be great, thanks

You have:

E=(1-u*)(1+u*)

This is a quadratic equation in u* \(\displaystyle \ \ \to \ \ \) solve for u* accordingly.

However, if you "play" with the equation - you could solve it in another (more intuitive) way.

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Correct - howeveru*=0, u*= sqrt(1-E), u*=-sqrt(1-E) ?

Why does your question use the term "biologically relevant"?

What is the significance of that term?

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No, do you remember what u denotes? can a population be negative?

u is denoting an animal population. So the steady state that is -sqrt(1-E) is biologically irrelevant as a population cannot be negative. The steady state 0 indicates the population of the animal species is extinct, and the positive sqrt steady state indicates an increase population?No, do you remember what u denotes? can a population be negative?

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It sounds good to me besides the last part. Drop the "increase", this is just a steady state solution (positive constant value which is biological relevant).u is denoting an animal population. So the steady state that is -sqrt(1-E) is biologically irrelevant as a population cannot be negative. The steady state 0 indicates the population of the animal species is extinct, and the positive sqrt steady state indicates an increase population?

great, thanks a lotIt sounds good to me besides the last part. Drop the "increase", this is just a steady state solution (positive constant value which is biological relevant).

to determine the stability, would you look at a phase line plot?It sounds good to me besides the last part. Drop the "increase", this is just a steady state solution (positive constant value which is biological relevant).

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You need to write the equation for a perturbation solution based on the steady state that you just found: u(t)=uto determine the stability, would you look at a phase line plot?