## 160 Reputation

10 years, 331 days

## Making a 3d graph of a continuous piecew...

Maple 2018

Lang_2_output_as_tswitch_varies.mw

^ in this worksheet I have made a graph of a variable in a simple ODE against time (shown below), at t=150 a switch condition, in the worksheet called tswitch, changes the rates of change of the ODE.

I am thinking about afunction that maps tswitch->solution of the ODE and would like to visualise it as a 3d surface, but couldn't work it out in Maple

## Logscale bar chart...

Maple 2018

I have just made a bar graph in Visualising_numerous_derivatives_of_the_L2_model.mw

and i would like to set it to be logscaled, but could not find an option in the documentation, or a way of using a logplot to get similar functionality

## Plotting the derivatives of a varaible i...

Maple

Hi

I have made a worksheet showing how a variable, from an ode varies with time

I would like to make similar graphs for y',y'',y''' etc and i couldn't think of how to do it.

Additionally I wanted to plot a bar graph of  y^(i)(1000)-lim(t approaches 1000 from below of y) any ideas oin how to do that?

thanks

## Visualising solutions to sums of polynom...

Maple 2018

I'm working towards creating a way to visualise real polynomial ideals! (or at least the solutions of the polynomials in the ideals) this code creates a plot showing the solutions to all the polynomials in the ideal generated by P1 and P2 (these are specified in the code)

with(plots);
P1 := x^2+2*y^2-3;
solve(P1, y);
Plot1 := plot([%], x = -2 .. 2);

P2 := -2*x^2+2*x*y+3*y^2+x-4;
solve(%, y);
Plot2 := plot([%], x = -4 .. 2);

P2*a+P1;
solve(%, y);
seq(plot([%], x = -4 .. 2), a = 0 .. 10, .1);
display(%, Plot1, Plot2)

This is because when you multiply two polynomials their set of solution curves is just the union of the sets of curves associated with the previous polynomials.

For the next step I'd like to create a graph of the solutions associated with an ideal with three generators. To stop this from being excessively messy I'd like to do it with the RGB value of the colour of a curve is determined by  a and b where the formula for a generic polynomial that we are solving and graphing is given by:

P1+a*P2+b*P3;

where P3 is given by

P3 := x*y-3

I've tried various ways to use cury to make this work (my intuition is cury is the right function to use here)  but got no where. Any ideas how to procede?

## Understanding the ratios of limits of di...

Maple 2015

I have a system of ODEs with parameters, p[i], and variables, x[i].

f := [
-p[1]*x[1]^2+x[2],
-2*p[1]^2*x[1]^3+2*p[1]*x[1]*x[2]+x[1]+1
];

associated with the innitial conditions:
[x[1](0) = p[2], x[2](0) = p[3]].

I am interested in sets of parameters where the solution x[1](t) is the same; if [p[1],p[2],p[3]] is associated with a solution x(p,t), and [ph[1],ph[2],ph[3]] is asociated with the solution x(ph,t); then x[1](p,t)=x[1](ph,t) for all t if and only if

[ph[1] = ph[1],
ph[2] = p[2],
ph[3] = -p[1]*p[2]^2+p[2]^2*ph[1]+p[3]]

i.e. ph[1] takes any real value, ph[2] takes the same values as p[2] and ph[3] takes a value determined by the original parameter vector and ph[1].

In a previous question it was demonstrated that x[2](ph,t)/x[2](p,t) rapidly converge on p[1] as t increases for a specific parameter vector that was given in the question (see graph below)

This raises the question does this limit generally hold?

I have struggled to do this in maple and I am suspicious of the answer i have got
i.e.
limit (x[2](ph,t)/x[2](p,t),t=infinity)=+/- infinity

My question is
+ when does a finite limit exist?
+ what is the finite limit?

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