No idea how to approach this one

[luvs2spooge]

I need to substitute in [MATH]x =\frac{1}{[A]} [/MATH] and then show [MATH]\dot{x}[/MATH] in terms of [MATH]A[/MATH] via the chain rule, then show a derivation or [MATH]\dot{x}[/MATH]. So there should not be any [MATH][A][/MATH] left.

This is the equation that I have so far.

[MATH]\frac{1}{[A]^{2}}\times\dot{[A]} = \frac{\omega}{[A]}- \frac{\omega}{N} - \frac{\alpha}{[A]}[/MATH]

 

[Deleted member 4993]

I need to substitute in [MATH]x =\frac{1}{[A]} [/MATH] and then show [MATH]\dot{x}[/MATH] in terms of [MATH]A[/MATH] via the chain rule, then show a derivation or [MATH]\dot{x}[/MATH]. So there should not be any [MATH][A][/MATH] left.

This is the equation that I have so far.

[MATH]\frac{1}{[A]^{2}}\times\dot{[A]} = \frac{\omega}{[A]}- \frac{\omega}{N} - \frac{\alpha}{[A]}[/MATH]

Please explain:

what is [A]?

what is \(\displaystyle \omega\)?

 

[luvs2spooge]

Please explain:

what is [A]?

what is \(\displaystyle \omega\)?

Its a predator-prey type model N is population total and [MATH][A][/MATH] the prey population. [MATH]\omega[/MATH] and [MATH]\alpha[/MATH] are both rates and which the individuals transfer. these are both constants.

Its i made from the following equation.

 

[Cubist]

Its a predator-prey type model N is population total and [MATH][A][/MATH] the prey population. [MATH]\omega[/MATH] and [MATH]\alpha[/MATH] are both rates and which the individuals transfer. these are both constants.

Its i made from the following equation.

View attachment 16161

It's difficult to see why you'd substitute x=1/[A] into that.

By [A] do you mean modulus ( absolute value which is more commonly shown as |A| ). I would certainly expect that a population could never have a negative quantity in the wild

NB You can post a picture of the original problem if that will help to explain it.

 

[luvs2spooge]

It's difficult to see why you'd substitute x=1/[A] into that.

By [A] do you mean modulus ( absolute value which is more commonly shown as |A| ). I would certainly expect that a population could never have a negative quantity in the wild

NB You can post a picture of the original problem if that will help to explain it.

I also do not understand the purpose of substitution where x=1/[A].

I found the non-zero equilibrium to be [MATH]A^{*} = N(1-\frac{\alpha}{\omega})[/MATH]
I found this which looks similar to what I am trying to achieve but it is still not making much sense.