## 499 Reputation

12 years, 153 days

## Parameters...

How could I adjust that to see what happens for negative time? Perhaps through in animation.

## Thanks, that's better than...

Thanks, that's better than what I got from this thread:

http://www.mapleprimes.com/forum/phaseportrait#comment-14266

## Conditions with Maple...

And if I wanted to write a conditional statement

If the eigenvalues are real and have opposite signs

else If eigenvalues are both real with same sign

print node

else if  eigenvalues are both real with complex conjugate

print spirals

else if at least one of the eigenvalues is zero

print not an isolated fixed point

end

end

end

My issue is how would I get make to look at each eigenvalue for the above conditions?

## Nevermind...

I specified mu and got a nice answer.

thanks anyway

## Better yet...

> restart; mu := .96; 0.96 > ode := (D(theta))(t) = mu+sin(theta(t)); D(theta)(t) = 0.96 + sin(theta(t)) > dsolve(ode); / / 7 \ \ |4 exp|-- t| _C1 - 3 | | \25 / | theta(t) = -2 arctan|--------------------| | /7 \ | |-4 + 3 exp|-- t| _C1| \ \25 / / > ics := theta(0) = 0; theta(0) = 0 > dsolve({ics, ode}); Is there a better choice for IC?

## Assume...

restart; assume(mu,'real');is(0< mu<1); ODE:=(ⅆ)/(ⅆt)theta(t)=mu+sin(theta(t)); ans:=dsolve([ODE]); theta(t):= 2 arctan((tan(1/2 t sqrt(mu^2-1)+1/2 _C1 sqrt(mu^2-1)) sqrt(mu^2-1)-1)/(mu)); ics:=theta(0)=1,D(theta)(0)=0; dsolve([ODE,ics]); Gives me the error: Error, (in dsolve) required an indication of the dependent variables in the given system What's the problem?

## Nevermind I got it....

Nevermind I got it.

## PLot...

f := proc (r, x) options operator, arrow; r*x+x^3-x^5 end proc; with(plots) display([implicitplot(f(r, x), x = -2 .. 2, r = -1 .. -3*x^2+5*x^4, colour = blue, axes = box, gridrefine = 3, crossingrefine = 3), implicitplot(f(r, x), x = -2 .. 2, r = -3*x^2+5*x^4 .. 2, colour = red, axes = box, gridrefine = 3, crossingrefine = 3)]); display(plottools[rotate](%, 3*Pi*(1/2), [0, 0]), labels = [r, x]) How do I shorten the range in r to -1,2. I tried adjusting the variables but it still extends beyond r = 2 and I don't want all that garbage. Do you know how to shorten the range in r?

## Also how did you determine...

Also how did you determine the interval for r?

`r=cos(x) .. 2`

## When I try I get Error, (in...

When I try I get Error, (in plots/implicitplot) invalid input: invalid range for first variable

## Also how do I switch the...

Also how do I switch the axis, X on the vertical and r on the horizontal?

## BIFpt2 := [[-4/27, 1/3], [0,...

BIFpt2 := [[-4/27, 1/3], [0, 1]];

is useless,

how do I plot the equilibrium points?

## After you established your...

After you established your stable points, you are asked to draw the vector fields on the diagram.

I assume r would be the parameter for the animation.

## What if I want to plot the...

What if I want to plot the vector field for the following function? f := r*x-sin(x) I was only able to plot the above with this command: implicitplot(f = 0, r = -4 .. 4, x = -14 .. 14, style = POINT) How do I include this in the animate command?
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