Items tagged with phase

hello guys,

 

i have a system of autonomous equations which i want to plot its 3D phase space with directional field,

i have some problem with it :dy.mw , and i dont know how to command for add some directional field for 3D phase space .

 

thank you guys

 

Dear Maple users

An engineering student asked me how Maple is handling complex numbers in polar form. He told me that his fellow students are using another CAS, whereas he himself prefer Maple. When making calculations with AC currents having different phases the other students were using the easy notation depicted in the first line on the picture below. Obviously here the angle (argument) is measured in degrees. I tried to perform the same calculations in Maple, but found it to require a very heavy notation: the other three lines on the picture. Now my question is: Does it really have to be that messy, or maybe there are some package, which will accomplish the task in a more neat way? I mean it is a rather common operation in the engineering sciences.

NB! Of couse one can argue about the educational value of using the notation of the other CAS! From that viewpoint they will probably not learn anything ...

 

 

Regards,

Erik

 

Hi,

I am a Maple über noob.

I am strugeling to figure out how to do simple phase calculations

For example

Phase_angle.mw

It is mainly for 3-phase angle calculation

Hello!

To get the phase portrait, I did this

Eq1:=diff(x(t),t)=1-d*x(t)-x(t)*v(t);

Eq2:=diff(y(t),t)=-a*y(t)+x(t)*v(t)-y(t)*w(t);

Eq3:=diff(z(t),t)=-b*z(t)+y(t)*w(t);

Eq4:=diff(v(t),t)=-p*v(t)+y(t);

Eq5:=diff(w(t),t)=-q*w(t)+c*z(t);

d:=0.012:a:=0.93:c:=40:b:=5.6:p:=5.6:q:=5.6:
ics:=x(0)=5,y(0)=1,z(0)=2,v(0)=0.5,w(0)=4;

eq1:=1-d*x-x*v;
eq2:=-a*y+x*v-y*w;
eq3:=-b*z+y*w;
p:=5.6:
eq4:=-p*v+y;
eq5:=-q*w+c*z;

solve({eq1=0,eq2=0,eq3=0,eq4=0,eq5=0},{x,y,z,v,w});

initialset:={seq(seq(seq(seq(seq([x(0)=a1,y(0)=a2,z(0)=a3,v(0)=a4,w(0)=a5],a1=0..5),a2=0..1),a3=0..2),a4=0..0.5),a5=0..4)}:

A:=DEplot([Eq1,Eq2,Eq3,Eq4,Eq5],[x(t),y(t),z(t),v(t),w(t)],t=0..140,x=5..7,y=0..2,initialset,stepsize=0.01,color=blue,linecolor=magenta,arrows=medium,axes=boxed):

Error, (in DEtools/DEplot/WhichPlot) More than two dependent variables - please indicate the desired scene.

I want phase portrait projected on x − y plane.

Any comments?

If I have the following system of first order diff eq's:

x'(t)=2x(t)+3y(t)

y(t)=-3x(t)-2y(t)

then can I consider the coefficient matrix A=<<2,-3>,<3,-2>> and compute the eigenvalues of A and infer as follows:

if the eigenvalues are of the same sign- eq point is a node

if they are of opposite signs- eq point is a saddle

if they are pure imaginary- eq point is a center

if they are complex conjugates- eq. point is a spiral

I've been given these conditions but my text says for a linear system of the form x'=Ax, the eigenvalues of A can be used to identify the nature of the eq. point. I am confused as to whether this applies to the given system as well; I have obtained 5 different trajectories and drawn the phase diagram for the system


Hi there,
I have a set of differential equations whose solution, Jacobian matrix and its eigenvalues, direction field, phase portrait and nullclines, need to be computed.

Each of the equations has a varying parameter.

I know how to get the above for a single parameter value, but when I set a range of values for the parameters, Maple is not able to handle all cases as I would expect: solving the differential equation system:

eq1 := x*(1.6*(1-(1/100)*x)-phi*y)
eq2 := (x/(15+x)-0.3e-1*x-.4)*y+.6+theta
desys := [eq1, eq2];
vars := [x, y];
steadyStates := map2(eval, vars, [solve(desys)])

already yields an error:
Error, (in unknown) invalid input: Utilities:-SetEquations expects its 2nd argument, equations, to be of type set({boolean, algebraic, relation}), but received {-600*y+(Array(1..2, {(1) = 8400, (2) = 15900})), Array(1..5, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0})}


The equations are the following:
de1 := diff(x(t), t) = x(t)*(1.6*(1-(1/100)*x(t))-phi*y(t));
de2 := diff(y(t), t) = (x(t)/(15+x(t))-0.3e-1*x(t)-.4)*y(t)+.6+theta

the parameters being:
phi:=[0 0.5 1 1.5 2]
theta:=[5. 10.]

How can I handle the situation so that Maple computes each of the above for each combination of the parameters?

I would like to avoid using two for loops and having to store all results in increasingly bigger and complicated arrays.

The worksheet at issue is this: MaplePrimes_Tumour_model_phi_theta_variation.mw


Thanks,
jon

Hi there,

I would like to compute and display the nullclines of a set of ordinary differential equations.

AFAIK, I can compute the nullclines in Maple by defining the equations and solving the system

e.g.:

# Define the equations
eq1 := u(t)*(1-u(t)/kappa)-u(t)*v(t) = 0;
eq2 := g*(u(t)-1)*v(t) = 0;

# Solve the system (i.e. compute the nullclines)
sol := solve({eq1, eq2}, {u(t), v(t)});

However, I am not quite able to imagine how to display them over a dfieldplot or a phaseportrait.

Attached is an example with some differential equations, and their vector field and trajectories: MaplePrimes_Predator_prey_model_nullclines.mw.

It can be use to illustrate how to (compute and) display the nullclines.

 

Thank you,

jon

Hi all,

I have a simple transfer function like

 

 

I want to calculate the amplitude ratio and the phase shift.

Without maple I would set s=I*omega and solve for real and imaginary part to obtain the phase shift and amplitude ratio.

 

 

Is there any possibility to do that in Maple more easily?

 

 

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)};

DEtools[DEplot](Sys1,[N(t),P(t)],t=-10..10,N=0..2,P=0..2);

 

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);
d
--- y(t) = v(t)
dt
> eq2 := diff(v(t), t) = -3*v(t)+10*y(t);
d
--- v(t) = -3 v(t) + 10 y(t)
dt
> 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 muchmaple.mw

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:
x:=Vector(N+1):

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:

 dx/dt=x

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)];

with(DEtools);

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);
with(DEtools);
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...
1 2 Page 1 of 2