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Dear All,

I need your help to plot the phase portrait using DEtools[DEplot]  these are the lines of the code. But when I make RUN, there is an error. I need your help to fix the error. Many thinks.


r1:=1; r2:=1; q2:=2; q1=0.5;  a1:=1;

Sys1 := {diff(N(t),t) = r1*N*(1-N/q1)-P*N/(1+N), diff(P(t),t) = r2*P*(exp(-a1*P)-q2)+P*N/(1+N)};



Many thinks

Hi everybody,

i don't understand when i use these examples from the help:


DE1 := {diff(z(x), x) = y(x)*x, diff(y(x), x, x) = y(x)*z(x)};
DEplot3d(DE1, [y(x), z(x)], x = -2 .. 2, [[y(0) = 1, (D(y))(0) = 2, z(0) = 1]], y = -4 .. 4, obsrange = true, stepsize = 0.5e-1, iterations = 3, orientation = [-124, 72]);


and when i look on my screen i have a white cube without phase portrait so i don't understand...


Thanks! and sorry for my english i'm french...

> with(DETools);
> eq1 := diff(y(t), t) = v(t);
--- y(t) = v(t)
> eq2 := diff(v(t), t) = -3*v(t)+10*y(t);
--- v(t) = -3 v(t) + 10 y(t)
> phaseportrait([eq1, eq2], [y, v], t = 0 .. 10, [[y(0) = 0, v(0) = 1]], y = -10 .. 10, v = -10 .. 10, linecolor = blue);



why my phase portrait not working

hello guys , i have a 3D dynamical system , what can i do to have its phase space in poincare coordinates ? thanks so

Below is my code for solving a solution of three first order ODEs using the 4th-order Runge-Kutta method.

I have been able to successfully plot the solutions of each of the ODEs (x,y,z) against time t, however I am struggling to produce a plot in the three dimensional phase domain of x,y,z. Could anybody suggest what commands to use as everything I have tried (plot, plot3d, implicitplot3d etc) has produced an error. 

h:= 0.01:
N:= 200:

Hey, I have a system of ODE and I can't draw it's phase curve. I tried to use DEplot and phaseportrait, but it doesn't work. Here is my system:


dy/dt=ky              (k is a constant)


Here is my piece of code:

DE := [diff(x(t), t) = x(t)];

DF := [diff(y(t), t) = k*y(t)];


phaseportrait([DE, DF], [y, x], t = -5 .. 5, y = -5 .. 5, x = -5 .. 5, k...

Hey, I'm trying to plot the phase curve of the simple system of ODE, BUT it shows me an error which one I don't understand at all :)

Here is my code:

DE := diff(x(t), t) = x(t);
DF := diff(y(t), t) = k*y(t);
phaseportrait([DE, D], [y, x], t = -5 .. 5, [[y(0) = 1, x(0)], [y(0) = 0, x(0) = 2], [y(0) = 0, z(0) = -2]], y = -5 .. 5, x = -5 .. 5, color = black, linecolor = red);

Error, (in DEtools/phaseportrait) invalid initial...


I am trying to do a phase plot of an autonomous system using DEplot command. However, no phase plot appears. Could you tell me what am I doing wrong? The same code worked for my professor in class, but it's not working for me. I am using Maple 16. The code is posted below.


> with DEtools

> sys := diff(x(t), t) = y(t), diff(y(t), t) = x(t)*(1-x(t)*x(t))+y(t);

> DEplot([sys], [x(t), y(t)], t = 0 .. 0.1e-8, x = -3 .. 3, y = -3 .. 3, color = black)


I want  to make the phase plot of d(Z(t))/dt (along y) and Z(t) (along x axis). The initial conditiona are arbitrary. I only have one equation:

d(dz/dt)/dz = - (sqrt(d(z^2)/dt + 10^10 * z^2)*dz/dt + 10^(10)*z)/dz/dt

Is it still possible to make a phase space plot or do i need another equation?


I have the following problem:

My function is defined by the determinant of 2 Heun functions

If I plot the phase I get something which looks quite what I'm looking for.

To get a better result I thought I would manually carry out the Wronskian as far as possible...

Doing some manipulations I get another form of the Wronskian which in fact should give the same result...

the problem is it doesnt :-(

I've added the spreadsheet....

Hi everybody,

Does somebody has an idea about how to model the temperature of water during freezing ?

I mean, if you consider a certain mass of water and you put it, for example on a fridge. I don't consider the convection but only the diffusion, and I would like to model, if possible with an animation the temperature of the water (as a cube for the shape).

Normally, during the freezing I should observe a decrease of the temperature, then a freezing...

Hi everyone,


I have this differential equations:


2 2
l := t -> sqrt((x1(t) - x2(t)) + (y1(t) - y2(t)) )


I want to draw the phase portraits (x1(t...



I'm trying to plot a few phase portraits for this four equation system but maple wont let me...

> restart;

> s := 10; d[T] := 0.2e-1; k1 := 2.4*10^(-5); k2 := 3*10^(-3);
> N := 5; delt := .24; c := 2.4; T0 := 1; 


Can someone please help me? Thanks


I need to plot the phase portrait of a hamiltonian of 4-dimensional phase-space, and I have an adiabatic invariant, i.e. one of the momenta is conserverd. 

I don't know how to replace a constant for the conserved momentum and plot the 2-dimensional phase space.

I am writiing 

sys := {diff(Y1(t), t) = -(diff(K, y1)), diff(Y2(t), t) = -(diff(K, y2)), diff(y1(t), t) = diff(K, Y1), diff(y2(t), t) = diff(K, Y2)}

and using the DEplot tool as 


I would like to animate the solution to


y'(t)= -4x(t)


that passes through x(0)=2, y(0)=1 as it orbits (0,0). I need to include the phaseportrait as the background. Any ideas on how to accomplish this?



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