# Solving System of ODE using Geogebra

Umeshp shared this question 7 years ago

Hi

I am new to Geogebra. Could you please help me to make a simulation of Repressilator, which is a classical example of Dynamical Systems Biology.

Intro and MATLAB code here: http://sysmic.ac.uk/static/... --- (1)

Code in XPP here: http://www.math.uwaterloo.c... ---- (2)

I would like to make a similar one in Geogebra

The purpose is to teach Dynamical Systems in Biology using repressilator as a case. I tried in geogebra (file attached). But not getting graph as expected in (1)

https://ggbm.at/568755 1

Hi,

Have a look at this one http://www.geogebratube.org/student/m93908 for an example of how to define your functions.

Basically you define functions m1prime etc to be functions of m1, m2, m3, p1, p2, p3 and t. Then use the NSolveODE-command 1

to

Is It correct. Yes or No?  1

BTW - I missed this was your first post. Welcome to the Forum!

PS - a nice thing about GeoGebra is that you can have all your parameters as sliders and see what the effect of changing them does to your solutions. 1

Thank You very much for the reply

I have tried but couldn't succeed. :( :(

the code that I have tried is

[command]m1'(t, m1, p3) = α + γ / (1 + p3²) - m1

m2'(t, m2, p1) = α + γ / (1 + p1²) - m2

m3'(t, m3, p2) = α + γ / (1 + p2²) - m3

p1'(m1, p1) = ß (m1 - p1)

p2'(m1, p1) = ß (m2 - p2)

p3'(m1, p1) = ß (m3 - p3)

a=0.03

γ=268.2

ß=0.2

[/command]

But I couldn't get the graph as expected. :( :(

https://ggbm.at/568781 1

A couple of points:

ALL functions should be defined as functions of ALL functions (and time). Thats what held you back mostly.

Minor Typo for p2 and p3 created numbers rather than defining functions.

Nice model, thankt for contributing. Working file attached.

https://ggbm.at/568783 1

Ooops - speaking of typos - change the name of p2 in my file to to p2'. Doesn't affect solutions very much, but is still wrong! Sorry. 1

Thank you very much

I have

f'(x, y) = 10 / (1 + x⁴) - y

g'(x, y) = 10 / (1 + y⁴) - x

I need to plot graph in nullcline

that is

f'(x,y)=0 and g'(x,y)=0

I tried. Please find the geogebra attached file.

I got a different graph when i did it in scilab (Fig- result.jpg attached)

https://ggbm.at/568799  1

Hi,

What you have done is solve the system of linear differential equations. This gives you f(x,y) and g(x,y).

The nullcline are plots which show for which values y and x give rise to f'(x,y) = 0 and g'(x,y) = 0. Thus, they are different functions, lets call them y = Nf(x) and y = Ng(x).

These are not obtained from some toolbox, but from simpel algebra. if f'(x,y) = 0 then y = 10(1 + x^4). Presto.

In the attachment I have used Graphics Window 2 to draw them, but as I said, there is no agic involved. You have to solve the algebra yourself (though you could do it in the CAS section of GeoGebra if you wish... Solve[10/(1-y^4) - x = 0, y]

https://ggbm.at/568803 1

Thanks

I missed the simple algebra. :( :( Thanks once again.

Feeling great for being here :) :P 1

Hi,

you can "see" in 3D view...

https://ggbm.at/568809 1

That was a really nice representation - Thanks. I like it when 3D suddenly connects things. :D