Calculating Null Clines: Tips & Tricks

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In summary, the conversation discusses the process of calculating the null clines for two given equations. The first equation is factored and solved for the variable u, resulting in two possible values. The second equation is also factored and solved for the variable v, giving two possible values. The conversation concludes by discussing the u and v null clines.
  • #1
mt91
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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 factorised out v to get:
\[ v(bu-c)=0 \]

giving me v=0 and bu-c = 0.

I'm not entirely sure if I'm going about this the correct way so any help would be appreciated, cheers
 
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  • #2
$u(1-u)(a+u) - uv = 0$

$u[(1-u)(a+u) - v] = 0$

$-u[u^2+(a-1)u - (a - v)] = 0$

$u = 0$, $u = \dfrac{(1-a) \pm \sqrt{(a-1)^2 + 4(a-v)}}{2}$

I'll leave what happens from here to you.
 
  • #3
skeeter said:
$u(1-u)(a+u) - uv = 0$

$u[(1-u)(a+u) - v] = 0$

$-u[u^2+(a-1)u - (a - v)] = 0$

$u = 0$, $u = \dfrac{(1-a) \pm \sqrt{(a-1)^2 + 4(a-v)}}{2}$

I'll leave what happens from here to you.

Nice, so that's the u null clines?

are the v null clines then when:

\[ dv/dt =buv-cv \]
\[ 0=buv-cv \]
\[ 0=v(bu-c) \]
\[ v=0, bu=c \]
 

FAQ: Calculating Null Clines: Tips & Tricks

1. How do I calculate null clines?

To calculate null clines, you will need to set up a system of equations and solve for the points where each equation equals zero. These points will be the null cline intersections.

2. What are some tips for calculating null clines?

One tip is to start by graphing the equations to get an idea of where the null cline intersections might be. Another tip is to use algebraic techniques, such as substitution or elimination, to solve for the null cline points.

3. How do I know if my calculated null clines are correct?

You can check your work by plugging the null cline points back into the original equations and making sure they equal zero. Additionally, you can graph the null clines and see if they intersect at the expected points.

4. Can I use software to calculate null clines?

Yes, there are many software programs, such as MATLAB or Mathematica, that can help you calculate null clines. However, it is important to understand the underlying mathematical concepts and not solely rely on the software.

5. Are there any tricks for simplifying the calculation of null clines?

One trick is to look for patterns or symmetries in the equations that may make solving for the null cline points easier. Another trick is to use approximation techniques, such as linearization, to simplify the equations before solving for the null cline points.

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