Advanced Search

Math-dashti

95 Reputation

4 Badges

0 years, 39 days
Contact Math-dashti

MaplePrimes Activity


These are questions asked by Math-dashti

How plot chaotic in maple?...

Math-dashti 95 Maple 2024
ode homework differential-equations
June 26 2025
1 3

i have a system but i don't know how i can plot chaotic or is need time for ploting or not ?

Find the jacobian matrix in two differen...

Math-dashti 95 Maple 2024
ode homework differential-equations
June 25 2025
1 7

Regarding to this equation i want to do the same as paper did, but i am not sure how i can determine the both  point in plot and how thus point show effect of system of equation and  how find jacobian in the two different point  i think he find it in general but i think we have to find it for each one  of equalibriom point  or we just find in general .
thus plot also are emazing did he use special code in matlab or mathematica? there is some app for plot thus kind of phase portrait but they not like this this is must have a special code for plotting in matlab or mathematica

> 

restart
> 

with(PDEtools)
> 

undeclare(prime, quiet)
> 

with(LinearAlgebra)
> 

declare(u(x, t), quiet); declare(U(xi), quiet); declare(V(xi), quiet)
> 

NULL
> 

DU := V

V

 (1)
> 

DV := U^2*beta/(delta*k^2)+(alpha*w/(delta*k^3)+1/(delta*k^2)-w^2/(delta*k^4))*U

U^2*beta/(delta*k^2)+(alpha*w/(delta*k^3)+1/(delta*k^2)-w^2/(delta*k^4))*U

 (2)
> 

var := U, V

U, V

 (3)
> 

J := Student:-MultivariateCalculus:-Jacobian([DU, DV], [var], 'output' = 'matrix')

Matrix(%id = 36893490902008029780)

 (4)
> 

Eigenvalues(J, implicit, output = 'list')

[RootOf(_Z^2*delta*k^4-2*U*beta*k^2-alpha*k*w-k^2+w^2, index = 1), RootOf(_Z^2*delta*k^4-2*U*beta*k^2-alpha*k*w-k^2+w^2, index = 2)]

 (5)
> 

Eigenvalues(J)

Vector[column](%id = 36893490902007993756)

 (6)
> 

NULL
> 

NULL
> 

DU1 := V

V

 (7)
> 

V = solve(DU1, V)

V = 0

 (8)
> 

DV1 := U^2*F[2]+U*F[1]

U^2*F[2]+U*F[1]

 (9)
> 

U = solve(DV1, U)

U = (0, -F[1]/F[2])

 (10)
> 

so*we*have*three*equalibriom*point*(0, 0)

so*we*have*three*equalibriom*point*(0, 0)

 (11)
> 

J1 := Student:-MultivariateCalculus:-Jacobian([DU1, DV1], [var], 'output' = 'matrix')

Matrix(%id = 36893490902007256836)

 (12)
> 

Eigenvalues(J1, implicit, output = 'list')

[RootOf(-2*U*F[2]+_Z^2-F[1], index = 1), RootOf(-2*U*F[2]+_Z^2-F[1], index = 2)]

 (13)
> 

Eigenvalues(J1)

Vector[column](%id = 36893490901938203092)

 (14)
 

NULL

Download bi-1.mw

Can plot the matrix instead of linear sy...

Math-dashti 95 Maple 2024
matrix ode homework
June 10 2025
2 4

in thus example all of them are write in shape of matrix but all of them are linear differential equation which have critical point zero ,i want to plot thus example and decided the kind of critical point by eagenvalue and by eagenvector i can find the trajectory how i can plot by matrix of each example and show that that critical point is which type as mention in picture?

system-phase-examples.mw

there is anyway for plot system of ode ...

Math-dashti 95 Maple 2024
ode homework differential-equations
June 09 2025
1 0

i want plot like that but i can't  and there is anyway for finding the equalibriom point of system? 

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

with(DEtools)
> 

with(DynamicSystems)
> 

sys := {diff(x(t), t) = 2*x(t)+3*y(t), diff(y(t), t) = 2*x(t)+y(t)}

{diff(x(t), t) = 2*x(t)+3*y(t), diff(y(t), t) = 2*x(t)+y(t)}

 (1)
> 

fns := {x(t), y(t)}

{x(t), y(t)}

 (2)
> 

sol := dsolve(sys, fns)

{x(t) = c__1*exp(4*t)+c__2*exp(-t), y(t) = (2/3)*c__1*exp(4*t)-c__2*exp(-t)}

 (3)
> 

ode := [diff(x(t), t) = 2*x(t)+3*y(t), diff(y(t), t) = 2*x(t)+y(t)]; S := dsolve(ode)

[diff(x(t), t) = 2*x(t)+3*y(t), diff(y(t), t) = 2*x(t)+y(t)]

  

{x(t) = c__1*exp(4*t)+c__2*exp(-t), y(t) = (2/3)*c__1*exp(4*t)-c__2*exp(-t)}

 (4)
> 

Student:-ODEs:-ODESteps(ode, {x(t), y(t)})

"[[,,"Let's solve"],[,,[(ⅆ)/(ⅆt) x(t)=2 x(t)+3 y(t),(ⅆ)/(ⅆt) y(t)=2 x(t)+y(t)]],["•",,"Define vector"],[,,x(t)=[?]],["•",,"Convert system into a vector equation"],[,,(ⅆ)/(ⅆt) x(t)=[?]*x(t)+[?]],["•",,"System to solve"],[,,(ⅆ)/(ⅆt) x(t)=[?]*x(t)],["•",,"Define the coefficient matrix"],[,,A=[?]],["•",,"Rewrite the system as"],[,,(ⅆ)/(ⅆt) x(t)=A*x(t)],["•",,"To solve the system, find the eigenvalues and eigenvectors of" A],["•",,"Eigenpairs of" A],[,,[[-1,[?]],[4,[?]]]],["•",,"Consider eigenpair"],[,,[-1,RTABLE(18446744074191517278,MATRIX([[-1], [1]]),Vector[column])]],["•",,"Solution to homogeneous system from eigenpair"],[,,(x)[1]=[]],["•",,"Consider eigenpair"],[,,[4,RTABLE(18446744074192645174,MATRIX([[3/2], [1]]),Vector[column])]],["•",,"Solution to homogeneous system from eigenpair"],[,,(x)[2]=[]],["•",,"General solution to the system of ODEs"],[,,x=`c__1` (x)[1]+`c__2` (x)[2]],["•",,"Substitute solutions into the general solution"],[,,x=[]+[]],["•",,"Substitute in vector of dependent variables"],[,,[?]=[?]],["•",,"Solution to the system of ODEs"],[,,{x(t)=-`c__1` (e)^(-t)+(3 `c__2` (e)^(4 t))/2,y(t)=`c__1` (e)^(-t)+`c__2` (e)^(4 t)}]]"

 (5)
 

NULL

Download Plot-1.mw

1 2 3 Page 3 of 3