Recent content by mt91

I've got this question here, I know to calculate steady states you set dn/dT and dc/dT to 0 and then solve. However can anyone help me understand what it means by the "two cases" and how you go about this?

I was wondering if anyone could help me clarify which null cline solutions are correct for this question I've got: I've got two differential equations: \[ du/dt =u(1-u)(a+u)-uv \] \[ dv/dt = buv-cv \] where a, b and c are constants. I know to find the u null clines you set du/dt to 0. \[...

Is anyone able to help with a diffusion-driven instability condition question I've got: I think I've got the DDI's: So DDI 1 = -pi^2 DDI 2 = 6pi^2 DDI 3= 7pi^2 DDI4 = 49^4 Which I believe satisfies the DDI conditions, however I'm not sure what it means by calculate the range of unstable...

I've got two differential equations I need to non-dimensionalise I've managed to do the \[ dc/dT=α- μc \] with the following working out: By letting: \[ N=N0n \] \[ C=C0c \] \[ t=t0T \] However I'm struggling with the first equation. I'm up to here, it's just the left hand side of the...

Nice, so that's the u null clines? are the v null clines then when: \[ dv/dt =buv-cv \] \[ 0=buv-cv \] \[ 0=v(bu-c) \] \[ v=0, bu=c \]

I need to calculate the null clines of these two equations. I know that in order to find the null cline you set the equations to 0. I tried to calculate the du/dt equation and got up to \[ a+u-au-u^2 -v=0 \] Not entirely sure where I'm supposed to go from there. For the dv/dt equation I...

I've got a question here which I'm really unsure what the wording is asking me to do, I've calculated (5), so worked out the steady states. However question 6 has really thrown me off with it's wording, any help would be appreciated.

I've got 2 questions here. I was able to work out question 5 and calculate the steady states. However for question 6 I've got no idea with the wording of the equation and where you would start, so any sort of help would be really helpful, cheers

I got 3 steady states, as u=0, u=1 and u=-a? and then by plotting u(1-u)(a+u), indicated from the graph that u=-a is stable, u=0 is unstable and u=1 is stable. Not sure what you mean by looking at the cases for a, so are you ok to explain that?

Thanks, do you know much about how you would interpret relevant steady states? So the steady state equation was about an animal population. If a steady state is 0 is this indicating that there's no population? and the negative square root steady state is indicating a decline in the population?

Meaning therefore we have 3 steady state solutions? \[ u*=0 \] \[ u*=sqrt(1-E) \] \[ u*=-sqrt(1-E) \] Thanks for your help by the way

Got a steady state question and was wondering if anyone would be able to check if I'm on the right track? Find the steady states of these two equations: My working out as far: \[ 0=u*(1-u*)(a+u*)-u*v* \] \[ 0=v*(bu*-c) \] I looked at the 2nd equation first giving: \[ v*=0, u*=c/b \]...

Cheers, it was the wording of the question I struggled with, because it said as a function of E. So this is what I did: \[ Eu*=u*(1-u*)(1+u*) \] \[ E=(1-u*)(1+u*) \] \[ ∴u*=1-E, u*=E-1 \] I think that u*=0 would be a solution, but I'm not sure with the wording of "function of E" what it wants...

Anyone able to calculate the steady states?

Any help would be appreciated